A person plans to use 128 feet of fencing to enclose a rectangular play area. What dimensions of the rectangle would maximize the area? What is the area?

Answer 1

(128/4)^2 = 32^2 = 1024 square feet = maximum area

the maximum area for a rectangle with a fixed perimeter is a square

each side of the square = 1/4 of the perimeter

the area of the square is the side squared

or use calculus

P= 2L + 2W = 128

L + W = 64

L= 64-W

A = LW = (64-W)W = 64W -W^2

take the derivative and set = 0

A'(W) = 64 -2W = 0

2W = 64

W = 64/2 = 32 feet wide

L=64-W = 64-32 = 32 feet long