The area of the rectangle is 36 in. the perimeter of the rectangle is 36 in write an equation using only one variable

The perimeter of a rectangle is twice the length plus twice the width. Thus,

2w + 2l = 36.

2l = 36 - 2w

l = 18 - w

The area is length times width.

36 = lw

36 = (18 - w) w

36 = 18w - w^2

w^2 - 18w + 36 = 0

w = (18 + - sqrt (18^2 - 4 * 36)) / 2

w = (18 + - sqrt (180)) / 2

w = 9 + - sqrt (45)

Thus, one of the side lengths is 9 + sqrt (45), and the other is 9 - sqrt (45).