A gardener has 1120 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.

Question

What dimensions would guarantee that the garden has the greatest possible area? 

shorter side: _____  ft (feet)

longer side: _____  ft (feet)

greatest possible area: _____  ft²  (square-feet)

Answer 1

L+2W=1120

Area = A = LW = (1120-2W)W = 1120W-2W^2

take the derivative and set = 0

A'=1120-4W = 0

solve for W

4W=1120

W=1120/4=280 feet

L=1120-2(280)=1120-560= 560 feet

Max Area = 280(560)= 156,800 square feet