The length of a rectangle is 8 inches more than the width. The perimeter is 32 inches. Find the length and width of the rectangle

P = 2 (L + W)

P = 32

L = W + 8

32 = 2 (W + 8 + W)

32 = 2 (2W + 8)

32 = 4W + 16

32 - 16 = 4W

16 = 4W

16/4 = W

4 = W < = = = width is 4 inches

L = W + 8

L = 4 + 8

L = 12 < = = = length is 12 inches

W = 4, l = 12

First, write down what you know.

l = w + 8

2l + 2w = 32

Now substitute (w+8) for l in the 2nd equation.

2 (w+8) + 2w = 32

Distribute the 2

2w + 16 + 2w = 32

Subtract 16 from both sides

2w + 2w = 16

Combine the w terms

4w = 16

Divide both sides by 4

w = 4

Now using the l = w+8 expression, substitute the known value for w

l = 4 + 8

l = 12

So w = 4, and l = 12