A farmer plans to use 340 feet of fencing and a side of her barn to enclose a rectangular garden​ (see the figure on the​ right). What dimensions of the rectangle would give the maximum​ area?

Question

A farmer plans to use

340

feet of fencing and a side of her barn to enclose a rectangular garden​ (see the figure on the​ right). What dimensions of the rectangle would give the maximum​ area? What is that​ area?



Answer 1

340 = 2W + L

L = 340-2W

Area = LW = (340-2W)W = 340W -2W^2

A' = 340-4W = 0

4W =340

W =340/4 = 85 feet wide

L = 340-2(85) = 340-170 = 170 feet long

maximum area = 85(170) = 14,450 ft^2