if the perimeter of a rectangle is 82ft........?

Question

if the perimeter or a rectangle is 82ft and the length is 15ft longer than the width. What are the length and width

Answer 1

x+x+x+15+x+15=82
4x+30=82
4x+30-30=82-30
4x=52
4x/4=52/4
x=13

length= 13+15=29
width=13

Answer 2

A rectangle's perimeter is given by
P = 2*L + 2*W
where L is the length and W is the width.

So, we know two things:
82 = 2*L + 2*W
2*L = 82 - 2*W
L = 41 - W

and

L - W = 15
L = W + 15

Since we've solved both equations for L, they must be equal to each other:
41 - W = W + 15
2*W = 26
W = 13 (ft)

From here, it's easy to see that
L = 28 (ft)