a daycare center has 40 ft of dividers with which to enclose a rectangular play space

Answer 1

IF you want to maximize the area of the rectangular play space, make it a square with each side = 40/4 = 10 feet

If you want more calculations to see why it's a square, take the formula for Area = A = LW

2L + 2W = perimeter = 40 feet

2L = 40- 2W

L = 20 - W

A=LW = (20-W)W = 20W - W^2

Area is maximized by taking the derivative and setting it equal to zero

A' = 20 - 2W = 0

2W = 20

W = 10

L = 20-W = 20-10 = 10

L=W = 10, which creates a square