algebra word problem

Question

A rectangle is 13 centimeters longer than it is wide. Its perimeter is 226 centimeters. Find its length and width.

Answer 1

For the rectangle, one pair of sides has length x and on pair of sides with length x+13.

The perimeter, then, is 2x + 2(x+13) = 2x + 2x + 26 = 4x + 26.

We are given 4x + 26 = 226.  Then 4x = 226 - 26 = 200. And x = 200/4 = 50.

So width is 50 and length is 50 + 13 = 63.

 

Check:  50 + 50 + 63 + 63 = 226.