What are the dimensions of a rectangle of maximum area whose perimeter is 92 feet

Answer 1

92/4 = 23 ft by 23 ft

Area = 23(23) = 529 square feet = max area

a square has the greatest area for a rectangle of given perimeter

P=2L+2W = 92

2L = 92-2W

L = (92-2W)/2 = (46-W)

Area = A = LW = (46-W)W = 46W - W^2

take the derivative and set equal to zero, solve for W

A' = 46 -2W = 0

2W = 46

W =23

L=46-23 = 23