Question

A farmer wants to enclose a rectangular field that borders a river with 400 feet of fencing material. if the farmer does not fence the side along the river, find the dimensions that will yield the maximum area. show all your equations.

Answer 1

Let each side perpendicular to the river be "x".Then the side parallel to the river is "400-2x".
The formula for Area = width*length
A(x) = x(400-2x)
A(x) = 400x - 2x^2
You have a quadratic with a = -2 and b = 400
Maximum Area occurs where x = -b/2a = -400/(2*-2) = 100 ft. (width)
length = 400-2x = 400-2*100 =  200 ft (length)