One way of doing this is by Analytic Geometry, by the properties of the parabola.

Another way, an easier way, is by Calculus. I will use this way here.

Rectangle.

Length = x ft.

Perimeter = 3000 ft.

So,

Width = (3000 -2x)/2 = 1500 -x ft.

a) Area, A = x(1500 -x) = 1500x -x^2

b) A is largest or smallest when dA/dx = 0

dA/dx = 1500 -2x

Set that to zero,

0 = 1500 -2x

2x = 1500

x = 1500/2 = 750 ft.

That should be the x for maximum A. (because minimum A is zero, and here x=0 or x=1500 ft.)

c) A = 1500x -x^2

max A = 1500(750) -(750)^2 = 562,500 sq.ft.

(Not 565,500 sq.ft.)