length - the measurement or extent of something from end to end

3 times the width plus 2 times the length

3 times the width plus 2 times the length
Let w be the width
Let l be the length
We have an algebraic expression of:
[B]3w + 2l[/B]

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section of a picture frame. Determine the area inside the wooden frame.
Area inside forms a square, with a length of 30 - 3 - 3 = 24. We subtract 3 twice, because we account for 2 rectangular strips with a width of 3.
Area of a square is side * side. So we have 24 * 24 = [B]576cm^2[/B]

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the length of shadow she will cast?
Set up a proportion of height to shadow length where s is the shadow length of the woman:
55/32 = 5.5/s
[URL='https://www.mathcelebrity.com/prop.php?num1=55&num2=5.5&den1=32&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
s = [B]3.2[/B]

7/4 yards represents 4/5 of the full length of rope. Find the length of the entire jump rope.

7/4 yards represents 4/5 of the full length of rope. Find the length of the entire jump rope.
Let the entire jump rope length be l. We're given the proportion:
4l/5 = 7/4
We type this in our search engine and our [URL='https://www.mathcelebrity.com/prop.php?num1=4l&num2=7&den1=5&den2=4&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] solves for l to get:
l = [B]2.1875 yards[/B]

A 124-inch length of ribbon is to be cut into three pieces. The longest piece is to be 36 inches lo

A 124-inch length of ribbon is to be cut into three pieces. The longest piece is to be 36 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon.
[LIST]
[*]Let the longest piece be l.
[*]The shortest piece is s = l - 36
[*]The third medium piece m = 0.5l
[/LIST]
We know s + m + l = 124. Now substitute for s and m
(l - 36) + 0.5l + l = 124
Combine like terms:
2.5l - 36 = 124
Type [URL='http://www.mathcelebrity.com/1unk.php?num=2.5l-36%3D124&pl=Solve']2.5l - 36 = 124 into our search engine[/URL], we get l = [B]64[/B]
Shortest piece s = 64 - 36 = [B]28[/B]
Medium piece m = 0.5(64) = [B]32[/B]

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twic

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
If the shorter piece is x, the longer piece is 20 - x
We also are given
15 - x = 2x + 3
Add x to each side:
3x + 3 = 15
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B3%3D15&pl=Solve']equation calculator[/URL], we get a shorter piece of:
[B]x = 4[/B]
The longer piece is:
15 - x
15 - 4
[B]11[/B]

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twic

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
If the shorter piece is x, the longer piece is 20 - x
We also are given
20 - x = 2x + 5
Add x to each side:
3x + 5 = 20
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B5%3D20&pl=Solve']equation calculator[/URL], we get a shorter piece of:
[B]x = 5
[/B]
The longer piece is:
20 - x
20 - 5
[B]15[/B]

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how t

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how tall is the tree?
Set up a proportion of height to shadow length where t is the height of a tree:
3/8 = t/15
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=t&den1=8&den2=15&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
t = [B]5.625[/B]

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of t

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need?
The difference between the 70 foot and 50 foot pole is:
70 - 50 = 20 foot height difference.
So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get:
hypotenuse = [B]36.06 feet[/B]

A 7 by 5 photo was enlarged. The length and width were enlarged 125%. Find the perimeter of the phot

A 7 by 5 photo was enlarged. The length and width were enlarged 125%. Find the perimeter of the photo.
Enlarge length 125%: 7 * 1.25 = 8.75
Enlarge width 125%: 5 * 1.25 = 6.25
Perimeter of the enlarged photo is 2l + 2w, so we have:
P = 2(8.75) + 2(6.25)
P = 17.5 + 12.5
P = [B]30[/B]

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?
Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that:
7 feet = 84 inches
So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']divide $3.36 by 84[/URL] to get the cost per inch:
$3.36/84 = [B]0.04 per inch[/B]

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the grou

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall?
We have a right triangle.
Hypotenuse is the rake length fo 74 inches. One of the legs is 70. We [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=70&hypinput=74&pl=Solve+Missing+Side']use our right triangle calculator to solve for the other leg[/URL]:
[B]24 inches[/B]

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in te

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in terms of x
Piece 1 + Piece 2 = 9
Piece 1 = x
x + Piece 2 = 9
Subtracting x from each side, we get:
x - x + Piece 2 = 9 - x
Cancel the x's on the left side, we get:
Piece 2 = [B]9 - x
[/B]
Check our work:
x + 9 - x ? 9
9 = 9

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the ot

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be?
The key phrase in this problem is [B]two pieces[/B].
Declare Variables:
[LIST]
[*]Let the short piece length be s
[*]Let the long piece length be l
[/LIST]
We're given the following
[LIST=1]
[*]s = l - 10
[*]s + l = 98 (Because the two pieces add up to 98)
[/LIST]
Substitute equation (1) into equation (2) for s:
l - 10+ l = 98
Group like terms:
2l - 10 = 98
Solve for [I]l[/I] in the equation 2l - 10 = 98
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 98. To do that, we add 10 to both sides
2l - 10 + 10 = 98 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
2l = 108
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2l/2 = 108/2
l = [B]54[/B]
To solve for s, we substitute l = 54 into equation (1):
s = 54 - 10
s = [B]44[/B]
Check our work:
The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10
Second check: Do both pieces add up to 98
54 + 44 ? 98
98 = 98

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purch

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet.
The area of a rectangle is length * width, so we have:
A = 290 * 150
A = 43,500 sq ft.
Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have:
Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag
Bags Needed = 43,500 / 300
Bags Needed = [B]145[/B]

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line cos

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line costs $2.00 per yard. How much would it cost to buy a new boundary line for the court?
[U]Approach:[/U]
[LIST]
[*]A volleyball court is shaped as a rectangle.
[*]And the boundary line runs on the perimeter of the rectangle.
[*]So we want the perimeter of the rectangle
[/LIST]
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=17&w=10&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 17 and width = 10[/URL], we have:
P = [B]54[/B]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree?
So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg.
The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides
Rearranging this equation to isolate a, we get a^2 = c^2 - b^2
Taking the square root of both sides, we get a = sqrt(c^2 - b^2)
a = sqrt(15^2 - 12^2)
a = sqrt(225 - 144)
a = sqrt(81)
a = [B]9 meters[/B]

A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that rep

A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that represents the length y (in feet) of a boa constrictor that is x years old.
8 inches per year = 8/12 feet = 2/3 foot
[B]y = 18 + 2/3x[/B]

A board must be cut into three pieces that are the same length. If it takes five minutes for each cu

A board must be cut into three pieces that are the same length. If it takes five minutes for each cut, how long will it take to saw the board into three pieces that are the same size?
Three equal pieces means only 2 cuts on the board:
2 cuts * 5 minutes per cut = [B]10 minutes[/B]

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be?
Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece:
[LIST=1]
[*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer)
[*]m = s + 6
[*]s + m + l = 57
[/LIST]
We substitute equations (1) and (2) into equation (3):
s + (s + 6) + (s + 9) = 57
Group like terms:
(1 + 1 + 1)s + (6 + 9) = 57
3s + 15 = 57
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]14
[/B]
[U]Plug s = 14 into equation 2 to solve for m:[/U]
m = 14 + 6
m = [B]20
[/B]
[U]Plug s = 14 into equation 1 to solve for l:[/U]
l = 14 + 9
l = [B]23
[/B]
Check our work for equation 3:
14 + 20 + 23 ? 57
57 = 57 <-- checks out
[B][/B]

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters off the end. How long is the piece of wood now?
When you saw off the end, the length decrease. So we subtract:
New length = Original length - Sawed piec
New length = 43.32 - 5.26
New length = [B]38.06[/B]

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches longer than the shorter. How long should each piece be
Let the shorter piece of board length be s. Then the larger piece is:
[LIST]
[*]l = s + 7
[/LIST]
And we know that:
Shorter Piece + Longer Piece = 25
Substituting our values above, we have:
s + s + 7 = 45
to solve this equation for s, we type it in our search engine and we get:
s = [B]19[/B]
Plugging this into our equation for l above means that:
l = 19 + 7
l =[B] 26[/B]

A cube is 1 meter long.What is the total length of all its edges?

A cube is 1 meter long.What is the total length of all its edges?
A cube has 12 edges.
12 edges x 1 meter for each edge = [B]12 meters[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?
Area of a cube is length times width:
A = 8 & 3/4 * 6 & 1/2
We need to convert these to improper fractions.
[LIST]
[*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4
[*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2
[/LIST]
Multiply the improper fractions together:
A = 35/4 * 13/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get:
[B]455/8 sq ft[/B]
If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get:
[B]56 & 7/8 sq ft[/B]

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v to find the volume. What was the volume of the tank?
1/2 foot = 6 inches
v = (6)^3
v = [B]216 cubic inches[/B]

A dresser has a length of 24 inches. What is the length of the dresser in centimeters?

A dresser has a length of 24 inches. What is the length of the dresser in centimeters?
[SIZE=5][B]Convert 24 inches to centimeters[/B][/SIZE]
centimeters = 2.54 x inches
centimeters = 2.54 x 24
centimeters = [B]60.96[/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants t

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Perimeter of a rectangle:
P = 2l + 2w
We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula
[B]165 = 2x + 2y where x > 50 and y <= 20[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be?
A flower bed has a rectangle shape, so the area is:
A = lw
We are given l = w + 3
Plugging in our numbers given to us, we have:
108 = w(w + 3)
w^2 + 3w = 108
Subtract 108 from each side:
w^2 + 3w - 108 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get:
w = (9, -12)
Since length cannot be negative, w = 9.
And l = 9 + 3 --> l = 12
So we have [B](l, w) = (12, 9)[/B]
Checking our work, we have:
A = (12)9
A = 108 <-- Match!

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print.
We subtract 5 cm from the length and the width to account for the frame:
Unframed Length: 80 - 5 = 75
Unframed Width: 65 - 5 = 60
Area of the unframed rectangle is:
A = lw
A = 75(60)
A = [B]4,500 sq cm[/B]

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per foot, what is the cost of the fencing for the garden?
Garden is a rectangle which has Perimeter P of:
P = 2l + 2w
l = 3w
P = 2(3w) + 2w
P = 6w + 2w
P = 8w
Width w = n, so we have:
P = 8n
Cost = 8n * 8 = [B]64n dollars[/B]

A gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs t

A gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs to purchase, if he makes 2round of fence Also find the cost of the rope, if it costs Rs4 per meter (take pie as 22/7)
Circumference of a circle = Pi(d).
Given Pi = 22/7 for this problem, we have:
C = 22/7(21)
C = 22*3
[B]C = 66[/B]

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 2

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot?
[U]Set up equations:[/U]
(1) 2l + 2w = 800
(2) l = 3w - 20
[U]Substitute (2) into (1)[/U]
2(3w - 20) + 2w = 800
6w - 40 + 2w = 800
[U]Group the w terms[/U]
8w - 40 = 800
[U]Add 40 to each side[/U]
8w = 840
[U]Divide each side by 8[/U]
[B]w = 105
[/B]
[U]Substitute w = 105 into (2)[/U]
l = 3(105) - 20
l = 315 - 20
[B]l = 295[/B]

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How fa

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How far away from the building should the bottom of the ladder be placed?
We have a right triangle, where the ladder is the hypotenuse, and the window side is one side.
Using our right triangle and the [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=24&hypinput=25&pl=Solve+Missing+Side']pythagorean theorem calculator[/URL], we get a length of [B]7 ft [/B]for the ladder bottom from the wall.

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the house will the ladder reach?
We have a right triangle with the hypotenuse as 4, the one leg as 2.5 We want to solve for the other leg length. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=2.5&hypinput=4&pl=Solve+Missing+Side']right triangle solver[/URL] to get [B]3.122[/B]

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line s

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line segment remains?
This means the leftover segment has a length of:
[B]26 - x[/B]

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. Wh

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. What is the length of each of the other two sides?
2 sides * 20 mm each is 40 mm
subtract this from the perimeter of 48:
48 - 40 = 8
Since the remaining two sides equal each other, their length is:
8/2 = [B]4mm[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides?
A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below:
P = 2l + 2w
We're given w = 17 and P = 54. So we plug this into the formula for perimeter:
2l + 2(17) = 54
2l + 34 = 54
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A park bench is 6 feet long. Convert the length to inches

A park bench is 6 feet long. Convert the length to inches
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']type in 6 feet into our search engine[/URL]. We get:
6 feet = [B]72 inches[/B]

A piece of pipe is 144 inches long. After 4 pieces, each 33 inches long are cut, what length of pipe

A piece of pipe is 144 inches long. After 4 pieces, each 33 inches long are cut, what length of pipe is left?
Calculate the length of cut pipe:
4 pieces * 33 inches per piece = 132 inches
The remaining pipe is found by subtracting the original pipe length by the cut pipe length:
144 - 132 = [B]12 inches[/B]

A pool is 5 meters wide and 21 meter long what is the area of the pool?

A pool is 5 meters wide and 21 meter long what is the area of the pool?
A pool is a rectangle. So the area for a rectangle is:
A = lw [I]where l is the length and w is the width.[/I]
[URL='https://www.mathcelebrity.com/rectangle.php?l=21&w=5&a=&p=&pl=Calculate+Rectangle']Plugging in our width of 5 and length of 21 to our rectangle calculator[/URL], we get:
A = [B]105 m^2[/B]

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area o

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area of the rectangle in terms of x.
Area of a rectangle (A) with length(l) and width (w) is expressed as follows:
A = lw
Plugging in our values given above, we have:
[B]A = (x - 7)(x + 5)[/B]

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of th

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of the rectangle.
w = n
l = 8.5n
P = 2(8.5n) + 2n
P = 17n + 2n
P = [B]19n[/B]

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSION

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE?
Whoa... stop screaming with those capital letters! But I digress...
The perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]P = 196
[*]l = 6w
[/LIST]
Plug these into the perimeter formula:
2(6w) + 2w = 196
12w + 2w = 196
[URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]w = 14[/B]
Now we put w = 14 into equation (2) above:
l = 6(14)
[B]l = 84
[/B]
So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14)
[/B]
Let's check our work by plugging this into the perimeter formula:
2(84) + 2(14) ? 196
168 + 28 ? 196
196 = 196 <-- checks out

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w
Given an area of 238 and a perimeter of 62, we have:
[LIST=1]
[*]lw = 238
[*]2(l + w) = 62
[/LIST]
Divide each side of (1) by w:
l = 238/w
Substitute this into (2):
2(238/w + w) = 62
Divide each side by 2:
238/w + w = 31
Multiply each side by w:
238w/w + w^2 = 31w
Simplify:
238 + w^2 = 31w
Subtract 31w from each side:
w^2 - 31w + 238 = 0
We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get:
w = (14, 17)
We take the lower amount as our width and the higher amount as our length:
[B]w = 14
l = 17
[/B]
Check our work for Area:
14(17) = 238 <-- Check
Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards b

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be?
Perimeter of a rectangle (P) with length (l) and width (w) is:
2l + 2w = P
We're given P = 506 and w = 100. We plug this in to the perimeter formula and get:
2l + 2(100) = 506
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get:
l = [B]153[/B]

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field?
We're given:
[LIST=1]
[*]l = w + 40
[/LIST]
And we know the perimeter of a rectangle is:
P = 2l + 2w
Substitute (1) into this formula as well as the given perimeter of 1120:
2(w + 40) + 2w = 1120
Multiply through and simplify:
2w + 80 + 2w = 1120
Group like terms:
4w + 80 = 1120
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 260[/B]

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width.
The area of a rectangle (A) is:
A = lw --> where l is the length and w is the width
We're given l = 2w, so we substitute this into the Area equation:
A = (2w)w
A = 2w^2
We're given the area of the pitch is 360, so we set:
2w^2 = 360
We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get:
w = [B]6*sqrt(5)
[/B]
Now we take this, and substitute it into this equation:
6*sqrt(5)l = 360
Dividing each side by 6*sqrt(5), we get:
l = [B]60/sqrt(5)[/B]

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room wi

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room with carpet that costs $76.00 per square yard. How much will it cost to recarpet the room? $
The area of a rectangle is length * width, so we have:
A = 5 yards * 4 yards
A = 20 square yards
Total cost = Cost per square yard * total square yards
Total Cost = $76 * 20
Total Cost = [B]$1520[/B]

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter?

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter?
The perimeter of a rectangle is:
P = 2l + 2w
Plugging in our length of 112 and our width of 68, we get:
P = 2(112) + 2(68)
P = 224 + 136
P = [B]360[/B]

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot?
The perimeter of a rectangle is: 2l + 2w = P.
We're given 2 equations:
[LIST=1]
[*]2l + 2w = 152
[*]l = w + 12
[/LIST]
Substitute equation (2) into equation (1) for l:
2(w + 12) + 2w = 152
2w + 24 + 2w = 152
Combine like terms:
4w + 24 = 152
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get:
w =[B] 32[/B]

A rectangular prism has a width of x feet, a length of y feet, and a height of h feet. Express its v

A rectangular prism has a width of [I]x[/I] feet, a length of [I]y[/I] feet, and a height of [I]h[/I] feet. Express its volume in square inches.
V = width * length * height
V = xyh
12 inches to a foot, so:
In cubic feet, we have 12 * 12 * 12 = 1728 cubic inches
V [B]= 1728xyh[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters
Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, we have:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 56
[/LIST]
Substitute equation (1) into equation (2) for l:
2(3w) + 2w = 56
6w + 2w = 56
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our math engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we substitute w = 7 into equation (1):
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room.
We're given two items:
[LIST]
[*]l = 3w
[*]P = 56
[/LIST]
We know the perimeter of a rectangle is:
2l + 2w = P
We plug in the given values l = 3w and P = 56 to get:
2(3w) + 2w = 56
6w + 2w = 56
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we plug in w = 7 that we just found into the given equation l = 3w:
l = 3(7)
l = [B]21
[/B]
So our dimensions length (l) and width (w) are:
(l, w) = [B](21, 7)[/B]

A room is 15 ft long and 12 feet wide. What are the length and width of the room in yards?

A room is 15 ft long and 12 feet wide. What are the length and width of the room in yards?
Since 3 feet = 1 yard, we have:
Length in yards = Length in feet / 3
Length in yards = 15/3
Length in yards = 5
Width in yards = Width in feet / 3
Width in yards = 12/3
Width in yards = 4

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per square yard. How much will the chalkboard cost?
Area of a chalkboard is denoted as :
A = lw
Given 1 yard width and 2 years length of the chalkboard, we have:
A = 2(1)
A = 2 square yards
Therefore, total cost is:
Total Cost = $27.31 * square yards
Total Cost = $27.31(2)
Total Cost = [B]$54.62[/B]

A square has a perimeter of 24 inches. What is the area of the square?

A square has a perimeter of 24 inches. What is the area of the square?
Perimeter of a square = 4s where s = the length of a side. Therefore, we have:
4s = P
4s = 24
Using our equation solver, [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D24&pl=Solve']we type in 4s = 24[/URL] and get:
s = 6
The problems asks for area of a square. It's given by
A = s^2
Plugging in s = 6, we get:
A = 6^2
A = 6 * 6
A = [B]36
[/B]
Now if you want a shortcut in the future, type in the shape and measurement you know. Such as:
[I][URL='https://www.mathcelebrity.com/square.php?num=24&pl=Perimeter&type=perimeter&show_All=1']square perimeter = 24[/URL][/I]
From the link, you'll learn every other measurement about the square.

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack
The lumber stack is a rectangular solid. The Volume V is found from the length (l), width (w), and height (h) by:
V = lwh
Plugging in our given values, we get:
V = 2 * 8 * 5
V = [B]80 cubic feet[/B]

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volley

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volleyball court
Plugging [URL='https://www.mathcelebrity.com/rectangle.php?l=60&w=&a=1800&p=&pl=Calculate+Rectangle']this into our rectangle calculator[/URL] and we get:
w = [B]30[/B]

A stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is

A stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is the tree?
Set up a proportion of wood height to shadow length where h is the height of the tree:
10/12 = h/96
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=10&num2=h&den1=12&den2=96&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = [B]80 feet[/B]

a string measures 20 inches is cut into pieces. Let z represent the length of one of the resulting p

a string measures 20 inches is cut into pieces. Let z represent the length of one of the resulting pieces. express length of the second piece in terms of the length z of the first pice
Second piece length = [B]20 - z[/B]

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 th

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 the length of the smaller base. If the perimeter of the trapezoid is 54.4 inches, what is the length of the smaller base of the trapezoid?
Setup measurements:
[LIST]
[*]Small base = n
[*]Large base = 1.2n
[*]sides = n/2
[*]Perimeter = n + 1.2n + 0.5n + 0.5n = 54.4
[/LIST]
Solve for [I]n[/I] in the equation n + 1.2n + 0.5n + 0.5n = 54.4
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 + 1.2 + 0.5 + 0.5)n = 3.2n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
3.2n = + 54.4
[SIZE=5][B]Step 3: Divide each side of the equation by 3.2[/B][/SIZE]
3.2n/3.2 = 54.4/3.2
n = [B]17[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2B1.2n%2B0.5n%2B0.5n%3D54.4&pl=Solve']Source[/URL]

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle?

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle?
First, we see if we can simplify. So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=16&num3=20&pl=GCF']type GCF(12,16,20) [/URL]and we get 4.
We divide the 3 side lengths by 4:
12/4 = 3
16/4 = 4
20/4 = 5
And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So [B]yes, this is a right triangle[/B].

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose the entire yard?
The yard is a rectangle. The perimeter of a rectangle is:
P = 2l + 2w where l is the length and w is the width.
Evaluating, using our [URL='https://www.mathcelebrity.com/rectangle.php?l=33.21&w=17.6&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get P = [B]101.62[/B]

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 tim

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 times his current length what will be his length be when he is full grown
Full Grown Length = Current Length * Growth Multiplier
Full Grown Length = 0.23 * 13
Full Grown Length = [B]2.99 meters[/B]

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length of 5.6 feet has a tail length of 4.9 feet. What is the tail length of an alligator whos body length is 4.8 feet
Set up a proportion of T/B
5.6/4.9 = t/4.8
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5.6&num2=t&den1=4.9&den2=4.8&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]t = 5.49[/B].

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of a

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and S = length of a side?
P = s + s + s
[B]P = 3s[/B]

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three tim

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon.
Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations:
[LIST=1]
[*]2l + 2m + s = 79
[*]m = s + 8
[*]l = 3s
[/LIST]
Substitute (2) and (3) into (1):
2(3s) + 2(s + 8) + s = 79
Multiply through and simplify:
6s + 2s + 16 + s = 79
9s + 16 = 79
[URL='https://www.mathcelebrity.com/1unk.php?num=9s%2B16%3D79&pl=Solve']Using our equation calculator[/URL], we get [B]s = 7[/B].
This means from Equation (2):
m = 7 + 8
[B]m = 15
[/B]
And from equation (3):
l = 3(7)
[B]l = 21[/B]

Arc Length and Area of a Sector of a Circle

Free Arc Length and Area of a Sector of a Circle Calculator - Calculates the arc length of a circle and the area of the sector of a circle

area of a rectangle

area of a rectangle
Let l be the length and w be the width of a rectangle. The Area (A) is:
A = [B]lw[/B]

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
Plugging our numbers in for P = 22 and L = 5, we get:
22 = 2(5) + 2W
22 = 10 + 2w
Rewritten, we have:
10 + 2w = 22
[URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get:
[B]w = 6[/B]

Cardioid

Free Cardioid Calculator - Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long is each piece of the rope?
Equal length means we divide the length of the rope by the number of equal cuts
[B]8/3 or 2 & 2/3 meters[/B]

Chord

Free Chord Calculator - Solves for any of the 3 items in the Chord of a Circle equation, Chord Length (c), Radius (r), and center to chord midpoint (t).

Each side of a square is lengthened by 3 inches . The area of this new, larger square is 25 square

Each side of a square is lengthened by 3 inches . The area of this new, larger square is 25 square inches. Find the length of a side of the original square.
area of a square is s^2
New square has sides s + 3, so the area of 25 is:
(s + 3)^2 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=%28s%2B3%29%5E2%3D25&pl=Solve']Solving for s[/URL], we get:
s = [B]2[/B]

Ellipses

Free Ellipses Calculator - Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity.

Euclidean Geometry

Free Euclidean Geometry Calculator - Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

Find the volume of the box. The box shows the length is 6 feet, the width is 4 feet, and the height

Find the volume of the box. The box shows the length is 6 feet, the width is 4 feet, and the height is 3 feet.
The shape is a rectangular solid. The Volume (V) is shown below:
V = lwh
V = 6 * 4 * 3
V = [B]72 cubic feet[/B]

Finding the dimensions

Expanded area = Original Area + area of Expansion
Area of Expansion = length expansion * width expansion

Frequency and Wavelength and Photon Energy

Free Frequency and Wavelength and Photon Energy Calculator - Provides the following 3 items using the speed of light and Plancks constant (h):

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
[IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG]
If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator
Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

Help on problem

[B]I need 36 m of fencing for my rectangular garden. I plan to build a 2m tall fence around the garden. The width of the garden is 6 m shorter than twice the length of the garden. How many square meters of space do I have in this garden?
List the answer being sought (words) ______Need_________________________
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____Need_________________________
List two formulas that will be needed_______Have_________________________
Write the equation for width_____________Have_________________________
Write the equation needed to solve this problem____Need____________________[/B]

Heptagon

Free Heptagon Calculator - Solves for side length, perimeter, and area of a heptagon.

Hexagon

Free Hexagon Calculator - This calculator solves for side length (s), Area (A), and Perimeter (P) of a hexagon given one of the 3 entries.

If 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be?
The perimeter of a rectangle P, is denoted as:
P = 2l + 2w
We're given l = 25, and P = 120, so we have
2(25) + 2w = 120
Simplify:
2w + 50 = 120
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 35[/B]

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, th

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width?
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given P = 44, so we substitute this into the rectangle perimeter equation:
2l + 2w = 44
We're also given w = 0.5l - 2. Substitute the into the Perimeter equation:
2l + 2(0.5l - 2) = 44
Multiply through and simplify:
2l + l - 4 = 44
Combine like terms:
3l - 4 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3l-4%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]l = 16[/B]
Substitute this back into the equation w = 0.5l - 2
w = 0.5(16) - 2
w = 8 - 2
[B]w = 6[/B]

If V is the volume of a cube whose side is s, express s in terms of V:

If V is the volume of a cube whose side is s, express s in terms of V:
We know the Volume (V) of a cube with side length s is:
V = s^3
Take the cube root of each side:
V^1/3 = (s^3)^1/3
s = [B]V^1/3[/B]

Jeremy ran 27 laps on a track that was 1/8 mile long. Jimmy ran 15 laps on a track that as 1/4 mile

Jeremy ran 27 laps on a track that was 1/8 mile long. Jimmy ran 15 laps on a track that as 1/4 mile long. who ran farther
[U]Calculate Jeremy's distance:[/U]
Distance = Laps * Track length
Jeremy distance = 27 * 1/8
Jeremy distance = 27/8
[U]Calculate Jimmy's distance:[/U]
Distance = Laps * Track length
Jeremy distance = 15* 1/4
Jeremy distance = 15/4
[COLOR=#000000]Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=27/8&frac2=15/4&pl=Compare']fraction comparison calculator[/URL], we see that [B]Jimmy [/B]ran farther[/COLOR]

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

Kamille is calculating the length of diagonal on a picture board and gets a solution of the square r

Kamille is calculating the length of diagonal on a picture board and gets a solution of the square root of 58. She needs to buy the ribbon to put across the diagonal of the board, so she estimates that she will need at least 60 inches of ribbon to cover the diagonal. Is she correct? Explain.
[URL='https://www.mathcelebrity.com/powersq.php?num=sqrt%2858%29&pl=Calculate']The square root of 58 [/URL]has an answer between 7 and 8.
So Kamille is [B]incorrect[/B]. She needs much less than 60 inches of ribbon. She needs less than 8 inches of ribbon.

Length (l) is the same as width (w) and their product is 64.

Length (l) is the same as width (w) and their product is 64.
We're given 2 equations:
[LIST=1]
[*]lw = 64
[*]l = w
[/LIST]
Substitute equation (2) into equation (1):
w * w = 64
w^2 = 64
[B]w = 8[/B]
Since l = w, then [B]l = 8[/B]

Moment of Inertia

Free Moment of Inertia Calculator - Calculates any of the 3 items from the Moment of Inertia equation, Inertia (I), Mass (M), and Length (L).

Mr. Jimenez has a pool behind his house that needs to be fenced in. The backyard is an odd quadrilat

Mr. Jimenez has a pool behind his house that needs to be fenced in. The backyard is an odd quadrilateral shape and the pool encompasses the entire backyard. The four sides are 1818a, 77b, 1111a, and 1919b in length. How much fencing? (the length of the perimeter) would he need to enclose the pool?
The perimeter P is found by adding all 4 sides:
P = 1818a + 77b + 1111a + 1919b
Group the a and b terms
P = (1818 + 1111)a + (77 + 1919b)
[B]P = 2929a + 1996b[/B]

P is twice the length plus twice the width

P is twice the length plus twice the width
Let the length be l. Let the width be w. The phrase [I]twice[/I] means we multiply by 2. We have:
[B]2l + 2w = P[/B]

Password Generator

Free Password Generator Calculator - This generates an alphanumeric password between a minimum and maximum character length that you specify.

Pentagons

Free Pentagons Calculator - Given a side length and an apothem, this calculates the perimeter and area of the pentagon.

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?
The perimeter P of a rectangle with length l and width w is:
2l + 2w = P
We're given P = 372 and l = 99, so we have:
2(99) + 2w = 372
2w + 198 = 372
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 198 and 372. To do that, we subtract 198 from both sides
2w + 198 - 198 = 372 - 198
[SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE]
2w = 174
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 174/2
w = [B]87[/B]

Polygons

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Rectangle Word Problem

Free Rectangle Word Problem Calculator - Solves word problems based on area or perimeter and variable side lengths

Rectangles and Parallelograms

Free Rectangles and Parallelograms Calculator - Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

Run Length Encoding

Free Run Length Encoding Calculator - Given a string, this will determine the run length encoding using repeating patterns of characters.

Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 606060 feet lon

I assume you want to know how many tiles or how many boxes of tile they need? I'll do both:
Since each tile covers the full 2 foot width of the walkway, we need to see how many tiles length wise we need.
60/2 = [B]30 tiles[/B] needed to cover the full walkway.
Now, each box contains 6 tiles, which means we need 30 tiles/6 tiles per box = [B]5 boxes of tiles[/B]

Sections of a rail way are 66m in length. What is the length of 81 placed to end to end?

Sections of a rail way are 66m in length. What is the length of 81 placed to end to end?
We have 81 sections x 66 meters per section = [B]5,346[/B]

Solve the problem

a confidence interval for a population mean has a margin of error of 0.081. Determine the length of the confidence interval

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis rope. Stacys rope is 23 feet long. Write and solve an equation to find the length t of Travis rope.
Let Stacy's rope be s. Travis's rope be t. We have:
s = 3t - 4
s = 23
So [B]3t - 4 = 23
[/B]
[URL='http://www.mathcelebrity.com/1unk.php?num=3t-4%3D23&pl=Solve']Paste this equation into our search engine[/URL] to get [B]t = 9[/B].

Strain

Free Strain Calculator - Solves for any of the 3 items in the strain equation: Change in Length, Strain, and Original Length

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width i

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
[LIST]
[*]length = [B]30 - x[/B]
[*]width = [B]18 + x[/B]
[/LIST]
b) Our new area using the lw = A formula is:
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
[B]-x^2 + 12x + 540 = 575[/B]
c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get:
[B]x = 5 or x = 7[/B]
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 mon

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph.
[IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG]
Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope.
Looking at a few points, we have:
(0, 20), (12, 30)
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of:
[B]5/6[/B]

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find th

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find the width of the flag.
for a rectangle, the Perimeter P is given by:
P = 2l + 2w
P[URL='https://www.mathcelebrity.com/rectangle.php?l=505&w=&a=&p=1520&pl=Calculate+Rectangle']lugging in our numbers for Perimeter and width into our rectangle calculator[/URL], we get:
l =[B] 255[/B]

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the peri

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches.
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given two equations:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 80
[/LIST]
We substitute equation 1 into equation 2 for l:
2(3w) + 2w = 80
6w + 2w = 80
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D80&pl=Solve']type it in our search engine[/URL] and we get:
w = 10
To solve for the length (l), we substitute w = 10 into equation 1 above:
l = 3(10)
l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120
We are also given:
(2) l = 3w - 6
Substitute equation (2) into equation (1)
2(3w - 6) + 2w = 120
Multiply through:
6w - 12 + 2w = 120
Combine like terms:
8w - 12 = 120
Add 12 to each side:
8w = 132
Divide each side by 8 to isolate w:
w =16.5
Now substitute w into equation (2)
l = 3(16.5) - 6
l = 49.5 - 6
l = 43.5
So (l, w) = (43.5, 16.5)

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangular word problem calculator[/URL], we have:
[LIST]
[*][B]l = 43.5[/B]
[*][B]w = 16.5[/B]
[/LIST]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangle word problem calculator[/URL], we get:
[LIST]
[*][B]w = 16.5[/B]
[*][B]l = 43.5[/B]
[/LIST]

the length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width

The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width.
Using our r[URL='http://www.mathcelebrity.com/rectangle.php?l=3&w=&a=&p=50&pl=Calculate+Rectangle']ectangle solver[/URL], we get [B]w = 10[/B].

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the wi

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the width?
l = 50.6
We are also given:
6w - 5.8 = 50.6
[URL='http://www.mathcelebrity.com/1unk.php?num=6w-5.8%3D50.6&pl=Solve']Typing this problem into the search engine[/URL], we get [B]w = 9.4[/B].

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²
The frame is a rectangle. The area of a rectangle is A = lw. So were given:
[LIST=1]
[*]l = w + 1
[*]lw = 12
[/LIST]
Substitute equation (1) into equation (2) for l:
(w + 1) * w = 12
Multiply through and simplify:
w^2 + w = 12
We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions:
w = 3
w = -4
Since width cannot be negative, we choose the positive result and have:
w = [B]3[/B]
To solve for length, we plug w = 3 into equation (1) above and get:
l = 3 + 1
l = [B]4[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.
Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
[LIST=1]
[*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I]
[*]2l + 2w = 72
[/LIST]
We substitute equation (1) into equation (2) for l:
2(3w + 4) + 2w = 72
Multiply through and simplify:
6w + 8 + 2w = 72
(6 +2)w + 8 = 72
8w + 8 = 72
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]8
[/B]
To solve for l, we substitute w = 8 above into Equation (1):
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters
A garden is a rectangle, which has perimeter P of:
P = 2l + 2w
With P = 72, we have:
2l + 2w = 72
We're also given:
l = 3w + 4
We substitute this into the perimeter equation for l:
2(3w + 4) + 2w = 72
6w + 8 + 2w = 72
To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get:
w =[B] 8[/B]
Now, to solve for l, we substitute w = 8 into our length equation above:
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length a

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width.
A flag is a rectangle shape. So we have the following equations
Since P = 2l + 2w, we have 2l + 2w = 60
l = 7w - 2
Substitute Equation 1 into Equation 2:
2(7w -2) + 2w = 60
14w - 4 + 2w = 60
16w - 4 = 60
Add 4 to each side
16w = 64
Divide each side by 16 to isolate w
w = 4
Which means l = 7(4) - 2 = 28 - 2 = 26

The longest bridge in america is 1700 ft long. Write an inequality that describes the length of ever

The longest bridge in america is 1700 ft long. Write an inequality that describes the length of every bridge.
Let the bridge length be b. Since no bridge will ever be greater than 1700 ft, we have:
[B]b <= 1700[/B]

The perimeter of a college basketball court is 102 meters and the length is twice as long as the wid

The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width?
A basketball court is a rectangle. The perimeter P is:
P = 2l + 2w
We're also given l = 2w and P = 102. Plug these into the perimeter formula:
2(2w) + 2w = 102
4w + 2w = 102
6w = 102
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]w = 17[/B]
Plug this into the l = 2w formula, we get:
l = 2(17)
[B]l = 34[/B]

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer than twice its width.
Let w be the width, and l be the length. We have:
P = l + w. Since P = 70, we have:
[LIST=1]
[*]l + w = 70
[*]l = 2w + 5
[/LIST]
Plug (2) into (1)
2w + 5 + w = 70
Group like terms:
3w + 5 = 70
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B5%3D70&pl=Solve']equation calculator[/URL], we get [B]w = 21.66667[/B]. Which means length is:
l = 2(21.6667) + 5
l = 43.33333 + 5
[B]l = 48.3333[/B]

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Fin

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle.
l = 4w - 15
Perimeter = 2l + 2w
Substitute, we get:
400 = 2(4w - 15) + 2w
400 = 8w - 30 + 2w
10w - 30 = 400
Add 30 to each side
10w = 370
Divide each side by 10 to isolate w
w = 37
Plug that back into our original equation to find l
l = 4(37) - 15
l = 148 - 15
l = 133
So we have (l, w) = (37, 133)

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is it’s width?
The formula for a rectangles perimeter P, is:
P = 2l + 2w where l is the length and w is the width.
Plugging in our P = 340 and l = 97, we have:
2(97) + 2w = 340
Multiply through, we get:
2w + 194 = 340
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B194%3D340&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]w = 73[/B]

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the dimensions
We are given the following equations:
[LIST=1]
[*]220 = 2l + 2w
[*]l = w + 30
[/LIST]
Plug (1) into (2)
2(w + 30) + 2w = 220
2w + 60 + 2w = 220
Combine like terms:
4w + 60 = 220
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B60%3D220&pl=Solve']Plug 4w + 60 = 220 into the search engine[/URL], and we get [B]w = 40[/B].
Now plug w = 40 into equation (2)
l = 40 + 30
[B]l = 70[/B]

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is its width?
Set up the rectangle perimeter equation:
P = 2l + 2w
For l = 69 and P = 250, we have:
250= 2(69) + 2w
250 = 138 + 2w
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B138%3D250&pl=Solve']equation solver[/URL], we get:
[B]w = 56 [/B]

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length?
Set up the perimeter (P) of a rectangle equation given length (l) and width (w):
2l + 2w = P
We're given P = 300 and w = 59. Plug these into the perimeter equation:
2l + 2(59) = 300
2l + 118 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 91[/B]

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. Wh

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Perimeter of a rectangle is:
P = 2l + 2w
We're given l = w + 3 and P = 54. So plug this into our perimeter formula:
54= 2(w + 3) + 2w
54 = 2w + 6 + 2w
Combine like terms:
4w + 6 = 54
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]
Plug this into our l = w + 3 formula:
l = 12 + 3
[B]l = 15[/B]

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, wh

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width?
The perimeter for a rectangle (P) is given as:
2l + 2w = P
We're given P = 258 and l = 71. Plug these values in:
2(71) + 2w = 258
142 + 2w = 258
[URL='https://www.mathcelebrity.com/1unk.php?num=142%2B2w%3D258&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 58[/B]

The perimeter of a square with side a

The perimeter of a square with side a
Perimeter of a square is 4s where s is the side length.
With s = a, we have:
P = [B]4a[/B]

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the length of each side
Let the first side be n.
Next side which is consecutive is n + 1
Next side which is consecutive is n + 1 + 1 = n + 2
So we have the sum of 3 consecutive numbers is 240.
We type in [I][URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutivenumbersis240&pl=Calculate']sum of 3 consecutive numbers is 240[/URL][/I] into our search engine and we get:
[B]79, 80, 81[/B]

The sum of the length l and 17

The sum of the length l and 17
The word [I]sum[/I] means we add:
[B]l + 17[/B]

The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the

The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the length of the trunk
Let p be the top part of the tree.
We have p = 3t.
Divide by 3, we get t = [B]p/3[/B]

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2
The Area (A) of a rectangle is given by:
A = lw
With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality:
4l < 86
To solve for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C86&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]l < 21.5[/B]

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is its angle of depression?
The sin of the angle A is the length of the opposite side / hypotenuse.
sin(A) = Opposite / Hypotenuse
sin(A) = 193.4 / 1090/3
sin(A) = 0.1774
[URL='https://www.mathcelebrity.com/anglebasic.php?entry=0.1774&pl=arcsin']We want the arcsin(0.1774)[/URL].
[B]A = 10.1284[/B]

Triangle Inequality

Free Triangle Inequality Calculator - This calculator displays 2 scenarios

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

Triangle with perimeter

What kind of triangle? Do you have side lengths? I need more information.

Vectors

Free Vectors Calculator - Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

What is the area of a triangular parking lot with a width of 200m and a length of 100m?What is the a

What is the area of a triangular parking lot with a width of 200m and a length of 100m?
Area of a Triangle = bh/2
Plugging in our numbers, we get:
Area of Parking Lot = 200(100)/2
Area of Parking Lot = 100 * 100
Area of Parking Lot = [B]10,000 sq meters[/B]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square?
Original square side length is s
Area = s^2
Double the side lengths to 2s
New area = (2s)^2 = 4s^2
Setup the difference relation:
4s^2 - s^2 = 432
3s^2 = 432
Divide each side by 3:
3s^2/3 = 432/3
s^2 = 144
s = [B]12[/B]