If there is 920 feet of fencing available, what is the maximum possible area of the pasture?

Question

The back of Tom's property is a creek. Tom 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 feet of fencing available, what is the maximum possible area of the pasture?

Answer 1

The area is LW

The perimeter is 2W + L which we are told is 920

So, using the perimeter equation, we can say 2W + L = 920 or L = 920 - 2W

Substituting "920 - 2W" into the area equation in place of L we get Area = (920 - 2W)W

Let Area = A

A(W) = (920 - 2W)W

A(W) = 920W - 2W²

The maximum will occur at the vertex. The vertex is found using -b/(2a) = -920/(2•(-2)) = -920/-4 = 230

For W = 230, the area = 920•230 - 2(230²) = 211600 - 105800 = 105800

So the maximum possible are is 105,800 square feet