Question

If 500 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to two decimal places.

Answer 1

500 = L + 2 w
so
L = 500 - 2 w

Area = L w = (500 - 2 w)w = 500 w - 2 w^2
where is vertex of that parabola?

2 w^2 - 500 w = - A

w^2 - 250 w = -(1/2) A

w^2 - 250 w + 125^2 = -(1/2) A + 15625

(w-125)^2 = -(1/2)( A - 31250)
so
A = 31250 at vertx