rectangle word problem | MathCelebrity Forum

# rectangle word problem

1. ### The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are th

The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are the dimensions? Set up 2 equations given P = 2l + 2w: l = 2w - 6 2l + 2w = 60 Substitute (1) into (2) for l: 2(2w - 6) + 2w = 60 4w - 12 + 2w = 60 6w - 12 = 60 To solve for w, type this into our...
2. ### The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensi

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions? We're given 2 equations: l = 3w P = 80 = 2l + 2w = 80 Substitute (1) into (2) for l: 2(3w) + 2w = 80 6w + 2w = 80 8w = 80 Divide each side by 8: 8w/8 = 80/8 w = 10 Substitute w = 10 into...
3. ### The diagonal of a rectangle is 10 inches long and the height of the rectangle is 8 inches. What is t

Draw this rectangle and you'll see we have a pythagorean theorem equation. a^2 + b^2= c^2 b = 8 and c= 10 a^2 + 8^2 = 10^2 a^2 + 64 = 100 Subtract 64 from each side: a^2 = 36 a= 6 Therefore, perimeter P is: P = 2l + 2w P = 2(6) + 2(8) P = 12 + 16 P = 28
4. ### 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 this into our rectangle calculator and we get: w = 30
5. ### 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 Step 1: Group constants: We need to group our constants 198...
6. ### 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 = lw
7. ### Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job? Area of platform which is a rectangle: A = lw A = 10 * 7 A = 70 Area of boards which are rectangles: A = lw A = 2...
8. ### 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...
9. ### 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: l = 3w 2l + 2w = 80 We substitute equation 1 into equation 2 for l: 2(3w) + 2w = 80 6w + 2w = 80...
10. ### 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: A = (x - 7)(x + 5)
11. ### 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...
12. ### 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 rectangle calculator, we get perimeter P: P = 34
13. ### 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...
14. ### 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: l = 3w 2l + 2w = 56 Substitute equation (1) into equation (2) for l: 2(3w) + 2w =...
15. ### 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 rectangle calculator, we get: l = 10
16. ### 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...
17. ### 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? Assumptions and givens: The poster has a rectangle shape l = 6 P = 20 The perimeter of a rectangle (P) is: 2l + 2w = P Plugging in our l and P values, we get: 2(6) + 2w = 20 Multiplying through and simplifying...
18. ### 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: l = w + 1 lw = 12 Substitute equation (1) into equation (2) for l: (w + 1) * w = 12 Multiply through and simplify: w^2 + w =...
19. ### 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: l = 3w + 4 (3 times the width Plus 4 since greater means...
20. ### 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...