length/width math problem

Question

You have 300 feet of fencing to enclose a rectangular lot. Find the dimensions of the rectangle that will maximize the enclosed area. What is the largest area that can be enclosed?

Answer 1

The answer to this question is that the rectangle with given perimeter and with the largest area is a square!

Prove it for this problem:

Perimeter = 300 = 2(L + W)

L = 150 - W

Area = A = LW = W(150 - W)

dA/dw = 2W - 150 and the derivative = 0 when W = 75, which makes L = 75 also.

QED