Question 92075
 
First there are more than one way to do it, since this is algebra.com, I will use quadratic equation to solve it.

Let x, y represent length and width of the rectangle.

 then we have x+y = 15

we need to find maximum area, A. A = length times width = xy

from x+y = 15, y = 15 - x

in A=xy, substitute y by  15 - x

A = x(15 - x)

{{{A = 15x -x^2}}}

this is a quadratic equation, the maximum value is at {{{ x = -15/(2*(-1))}}}

so x = 7.5, then y = 15 -x = 7.5

so it will be a square with length of 7.5 ft.