What is the maximum area that can be enclosed with 795 ft of fencing?

Question

A rectangular storage area is to be constructed along a side of a building. A security fence is required along the remaining three sides of the area. What is the maximum area that can be enclosed with 795 ft of fencing?

Length of the side parallel to the building is ___ ft

Length of the side perpendicular to the building is ___ ft

The maximum area of the storage area is ___ ft^2

Answer 1

A= LW

Perimeter = 795 = L + 2W

L = 795-2W

A = LW = (795-2W)W = 795W - 2W^2

take the derivative of A and set it equal to zero and solve for W to get the area maximizing width

A' = 795 - 4W = 0

4W = 795

W = 795/4 = 148 3/4 feet

L = 795- 397 1/2 = 397 1/2 feet

Maximum area = 397.5 x 148.75 = 59,128.125 square feet = 59,128 1/8 ft^2