Let P be the perimeter of the fence = 225
And ..... P = 2 ( Width + Length) .....so.....
225 = 2 (W+ L) divide by 2 in both sides
225 / 2 = W + L subtract W from both sides and simplify
112.5 - W = L (1)
And the area, A, = W * L
So
A = W * L ..... sub (1) for L
A = W * ( 112.5 - W) simplify
A = 112.5W - W^2 rewrite as
A = -W^2 + 112.5W
We have an "upside down" parabola and is the quadratic we need
The area will be maximized at the W value of -112.5 / [2 * -1] = 56.25
And using (1), the Length will be 112.5 - W = 112.5 - 56.25 = 56.25
So......the maximum area will be (56.25) * (56.25) = 3164.0625 sq ft.
Note that the area is maximized when we have a square with a side of 56.25 ft.....!!!