college algebra word problem

Question

Find the dimensions of the rectangular corral producing the greatest enclosed area given 320 feet of fencing. (Assume that the length is greater than or equal to the width.)

Answer 1

320/4 = 80 feet by 80 feet

largest rectangle with fixed perimeter is a square

Area = LW = [(320-2W)/2]W = (160-W)W = 160W - W^2

take the derivative and set equal to zero

A' = 160 -2W = 0

2W = 160

W = 160/2 = 80 feet

L = (320-2W)/2 = (320-160)/2 = 160/2 = 80 feet