Question

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

Answer 1

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).