Write and solve a system of linear equations to find the length and the width of a rectangle

The perimeter of a rectangle is 138 inches. The length exceeds the width by 65 inches. Find the length and width.

Solution

P = 2l + 2w

l = w + 65

Substitute 138 for P and w + 65 for l

138 = 2( w + 65) + 2w

138 = 2w + 130 + 2w

138 = 4w + 130

138 - 130 = 4w + 130 - 130

8 = 4w

8/4 = (4/4)w

2 = w

l = 2 + 65 = 67