What’s the maximum possible area of the pasture?

Question

The back of Jake’s property is a creek. Jake would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 200 feet of fencing available, what is the maximum possible area of the pasture?

Answer 1

Perimeter = 2 * width+ length

200 = 2w + L

200 - 2w = L

Area = length * width

A(w) = (200 - 2w)*w = 200w - 2w^2 = -2w^2 + 200w

a=-2 b = 0 c = 200

-b/(2a) = -200/(2*-2) = -200/-4 = 50

max area is (200 - 2*50) * 50 = 100*50 = 5000