How do you find the maximum area of a THREE sided enclosure with 250 feet of fencing?

Answer 1

L + 2w = 250 <--- 3 sides = 2 widths + 1 length

So L = 250 - 2w

Area = length x width

= (250 - 2w)w <--- the area is now a function of width, w

Area(w) = (250 -2w)w <--- must maximize this function

The max occurs at the AVERAGE of the solutions.

The solutions are w=0 and 250 -2w = 0

w=0 and 250 = 2w

125 = w

Average is (125+0)/2 = 125/2 = 62.5 = 62 and 1/2

The max width occurs at w=62.5

(250 - 62.5)*62.5 = 11718.75