She has purchased 84 feet of fencing to build a rectangular fenced-in space. What dimensions should she use to maximize the space the dogs will have to play outside? What will the area be?

Answer 1

84/4 = 21 feet for each side = L = W

84= 2(L+W) = 2L + 2W

L+W = 42

L= 42-W

dimensions are 21 by 21 feet

21^2 = 441 square feet is the maximum area for a rectangle with side 21

a square is the rectangle with maximum area for a given perimeter. 84 = the perimeter

Area = A = LW = (42-W)W = 42W -W^2

max area is when the derivative = 0

A' = 42-2W = 0

2W = 42

W = 21 feet in width

L= (84/2) - W = 42-21 = 21 feet in length