A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1080 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area.

Step-by-step explanation:

Let the length of the playground is L and width is W.

Perimeter = 2 (L + W)

1080 = 2 (L + W)

L + W = 540 ... (1)

Area, A = L x W

A = L (540 - L)

A = 540 L - L²

differentiate with respect to L.

dA / dL = 540 - 2 L

Put it equal to zero for maxima and minima

540 - 2L = 0

L = 270 feet

W = 540 - 270 = 270 feet