College algebra word problem

Question

Find the dimensions of the rectangular corral producing the greatest enclosed area given 240 feet of fencing. (Assume that the length is greater than or equal to the width.)

Answer 1

The rectangle with greatest area is a square where length = width

240/4 = 60

the dimensions are 60' x 60'

You could do this with calculus. Let W=width, L=length. 240 = 2(L+W), 120 = L+W

L=120-W, Area = LW = (120-W)W = 120W -W^2

To find maximum area take the first derivative & set = 0

A' = 120-2W=0

2W=120

W=60 feet

L=120-60 = 60 feet

Greatest area = 60 x 60 = 3600 square feet