Answer:
600ft x 1200ft
Step-by-step explanation:
Use derivative optimization to find the maximum area.
I'll call the two same sides "a", and the one different side "b"
The maximum perimeter (including 3 sides) is 2400 ft. so,
2400 = 2a + b
The area is length × width. so,
A = ab
Using substitution to combine the equations,
A = a × (2400 - 2a)
A = -2a² + 2400a
Find the maximum of A by finding the zeros of its derivative.
dA = -4a +2400
0 = -4a + 2400
The maximum occurs at a = 600
Substitute in the perimeter equation to find b.
2400 = 2(600) + b
b = 1200
600 x 1200
