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

Answer 1

length = x
width = w
x + 2 w = 200 so x = 2 (100-w)
A = x w = 2 (100-w)w
A = 200 w - 2 w^2
now I do not know if you do calculus but if you do
dA/dw = 0 at max = 200 - 4w
w = 50
x= 2(50) = 100
A = 5,000
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if you do not do calculus find vertex of parabola
A = 200 w - 2 w^2
w^2 -100 w = - A/2
w^2 -100 w + 50^2 = -A/2 +2500
(w-50)^2 = -1/2(A-5000)
vertex at w = 50 and A = 5,000 as we already knew from the calculus