The perimeter of a rectangle is 24 inches. Find the dimensions if it’s length is 3 inches greater than its width?

Question

The perimeter of a rectangle is 24 inches. Find the dimensions if it’s length is 3 inches greater than its width?

Answer 1

The perimeter of a rectangle is equal to the sum of its two widths and its two lengths. 2W + 2L = 24 inches. Since the the length is 3 inches greater than the width, we can express the length as W+3. This allows us to say:

2W + 2(W+3) = 24 inches. Expanding this expression, we get

2W + 2W + 6 = 24 inches; collecting like terms, we get 4W = 18. This means that W = 18/4 = 4 1/2 inches. So, if W = 4 1/2 inches, that means the the length is 4 1/2 + 3 = 7 1/2 inches.

As a check: 2(4 1/2) + 2(7 1/2) = 24.

9 + 15 = 24

24 = 24.

Answer 2

L = length

W = width

P = perimeter = 2L+ 2W

From the problem

2L+2W = 24. (eqn. 1)

L = 3+W (eqn. 2)

Substitute equation 2 into equation 1 and solve for W. You can then use equation 2 to solve for L.