A fencing is limited to 20ft in length . What is the maximum rectangular area that can be fenced in using two ?

a fencing is limited to 20ft in length . What is


the maximum rectangular area that can be


fenced in using two perpendicular corner


sides of an existing wall?|||Area A = LW


Perimeter P = 2L+2W, but two of the sides are already covered, so


P = L+W = 20


L = W鈥?0





substituting


W(W鈥?0) = A


A = W虏 鈥?20W


to get max or min, differentiate and set equal to zero


A' = 2W 鈥?20 = 0


2W = 20


W = 10 ft


L = 10 ft


A = 100 square feet|||you have 2 20 ft pieces of fence


perimeter = 40ft





10ft sq = 100sqft





circle of radius 6.366ft = 127.32 sq ft





so you get an icecream cone shape with (100 +127.32)/2 = 113.66 sq ft