perimeter - The distance around a shape or object

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 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 chalkboard is 3 feet tall and 4 feet long. What is its perimeter

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter
A chalkboard is a rectangle. So the perimeter is:
2l + 2w
Using [URL='https://www.mathcelebrity.com/rectangle.php?l=4&w=3&a=&p=&pl=Calculate+Rectangle']our rectangle calculator[/URL], we get:
P = [B]14[/B]

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallp

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallpaper border are needed to wrap around the entire room?
A rectangle has an Perimeter (P) of:
P = 2l + 2w
We're given l = 17 and w = 15. So we have:
P = 2(17) + 2(15)
P = 34 + 30
P = [B]64[/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 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 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 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 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 field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?
We are given or know the following about the rectangle
[LIST]
[*]l = 2w
[*]P = 2l + 2w
[*]Since P = 360, we have 2l + 2w = 360
[/LIST]
Since l = 2w, we have 2l + (l) = 360
3l = 360
Divide by 3, we get [B]l = 120[/B]
Which means w = 120/2
[B]w = 60[/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 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 piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of th

A rectangular piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of the piece of paper
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=10&w=7&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get perimeter P:
P = [B]34[/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.

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.
We're given the following:
[LIST]
[*]l = 3w
[/LIST]
We know the Perimeter (P) of a rectangle is:
P = 2l + 2w
Substituting l = 3w and P = 56 into this equation, we get:
2(3w) + 2w = 56
Multiplying through, we get:
6w + 2w = 56
(6 +2)w = 56
8w = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 7[/B]
Substitute w = 7 into l = 3w, we get:
l = 3(7)
[B]l = 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 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 dimension of the room.
We're given:
l = 3w
The Perimeter (P) of a rectangle is:
P = 2l + 2w
With P = 56, 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 search engine[/URL] and we get:
w = [B]7
[/B]
Now we plug w = 7 into equation (1) above to solve for l:
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimension of the room.
We're given:
[LIST]
[*]l = 3w
[*]P = 64
[/LIST]
We also know the perimeter of a rectangle is:
2l + 2w = P
We plugin l = 3w and P = 64 into the perimeter equation:
2(3w) + 2w = 64
Multiply through to remove the parentheses:
6w + 2w = 64
To solve this equation for w, we type it in our search engine and we get:
[B]w = 8[/B]
To solve for l, we plug w = 8 into the l = 3w equation above:
l = 3(8)
[B]l = 24[/B]

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimens

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
The perimeter of a rectangle is P = 2l + 2w. We're given two equations:
[LIST=1]
[*]l = 4w
[*]2l + 2w = 80. <-- Since perimeter is 80
[/LIST]
Plug equation (1) into equation (2) for l:
2(4w) + 2w = 80
8w + 2w = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B2w%3D80&pl=Solve']Plugging this equation into our search engine[/URL], we get:
w = [B]10[/B]
To get l, we plug w = 10 into equation (1):
l = 4(10)
l = [B]40[/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 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 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]

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 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]

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]

Decagon

Free Decagon Calculator - Solves for the side, perimeter, and area of a decagon.

Equilateral Triangle

Free Equilateral Triangle Calculator - Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

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]

Isosceles Triangle

Free Isosceles Triangle Calculator - Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

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]

Kites

Free Kites Calculator - This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10 feet, how many posts will she need?
Perimeter (P) of a square with side s:
P = 4s
Given s = 40, we have:
P = 4(40)
P = 160 feet
160 feet / 10 foot spaces = [B]16 posts[/B]

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.
Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)
Feet of fencing = n
Perimeter of square garden = n
Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16
Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d
Divide body tissues by pi:
d = n/pi
Radius = n/2pi
Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2
Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56
The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.
Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380
Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380
Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9
Nearest foot = [B]284[/B]

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]

Nonagon

Free Nonagon Calculator - Calculates the side, perimeter, and area of a nonagon

Octagon

Free Octagon Calculator - Calculate side, area, and perimeter of an octagon based on inputs

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.

Quadrilateral

Free Quadrilateral Calculator - Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

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.

Rhombus

Free Rhombus Calculator - Given inputs of a rhombus, this calculates the following:

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants i

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be?
Sheila wants:
[LIST=1]
[*]l =5w
[*]2l + 2w = 100 <-- Perimeter
[/LIST]
Substitute (1) into (2)
2(5w) + 2w = 100
10w + 2w = 100
12w = 100
Divide each side by 12
[B]w = 8.3333[/B]
Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Squares

Free Squares Calculator - Solve for Area of a square, Perimeter of a square, side of a square, diagonal of a square.

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 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 perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?
Using our[URL='https://www.mathcelebrity.com/rectangle.php?l=&w=4&a=&p=28&pl=Calculate+Rectangle'] rectangle calculator[/URL], we get:
l = [B]10[/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 poster is 20 feet. The poster is 6 feet tall. How wide is it?

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
[U]Assumptions and givens:[/U]
[LIST]
[*]The poster has a rectangle shape
[*]l = 6
[*]P = 20
[*]The perimeter of a rectangle (P) is: 2l + 2w = P
[/LIST]
Plugging in our l and P values, we get:
2(6) + 2w = 20
Multiplying through and simplifying, we get:
12 + 2w = 20
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get:
w = [B]4[/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 backyard is 162 feet. It is 52 feet long. How wide is it?

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?
We [URL='https://www.mathcelebrity.com/rectangle.php?l=52&w=&a=&p=162&pl=Calculate+Rectangle']use our rectangle solver to solve for w[/URL]. We get:
[B]w = 29[/B]

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
Set up the perimeter equation:
2l + 2w = P
Given P = 204 and l = 66, we have:
2(66) + 2w = 204
2w + 132 = 204
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/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 notecard is 16 inches. The notecard is 5 inches wide. How tall is it?

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?
Perimeter of a rectangle P is:
P = 2l + 2w
We have:
2l + 2w = 16
We are given w = 5, so we have:
2l + 2(5) = 16
2l + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B10%3D16&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]l = 3[/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 rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter for a rectangle is given below:
P = 2l + 2w
We're given l = 7 and P = 60. Plug this into the perimeter formula:
60 = 2(7) + 2w
60 = 14 + 2w
Rewritten, it's 2w + 14 = 60.
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/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 perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.
[LIST]
[*]h = b + 70
[*]A = 1/2bh = 3000
[/LIST]
Substitute the height equation into the area equation
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/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]

Trapezoids

Free Trapezoids Calculator - This calculator determines the following items for a trapezoid based on given inputs:

* Area of trapezoid

* Perimeter of a Trapezoid

* Area of trapezoid

* Perimeter of a Trapezoid

Triangle with perimeter

A triangle with a perimeter of 120.
What degree are the three sides?