The maximum area enclosed is a square, then the area will be :
side^2 = (perimeter/4)^2 = (200 feet/4)^2 = 50^2 feet^2 = 2500 feet^2.
We can prove that this is a square:
Call x one side, then the other side is: (200 -2x) / 2 = 100 - x
And the area , S = x(100-x) = 100x - x^2
Maximum area => S' = 0 = 100 -2x => 2x = 100 => x =100/2 = 50
=> 100 - x = 100 - 50 = 50.
Then, when showed that the two sides are equal to 50 feet, and the shape enclosed is a square with area = 2500 ft^2.
