A rectangular enclosure is to be constructed with 800 feet of fence in order to have four sections. What should be the dimensions in order to maximize the area enclosed? What is the maximum area?

Answer 1

Well, I bet it turns out to be a square but anyway:
A = b c where b is breadth and c is length

2 b + 2 c = 800
so
b + c = 400
c = (400 - b)
so
A = b * (400-b)
A = 400 b - b^2
b^2 - 400 b + A = 0
where is the vertex of this parabola (I assume you do not do calculus)
b^2 - 400 b = -A
b^2 - 400 b + 40,000 = -A + 40,000
(b-200)^2 = -A + 40,00
vertex (maximum) when b = 200
then c = 400-200 also = 200
just as we suspected