the dimensions of the playground that will enclose the greatest total area is 90*90 = 8100 feet
Let the length of the playground is L and width is W.
Perimeter = 2 (L + W)
360 = 2 (L + W)
L + W = 180 ... (1)
Area, A = L x W
A = L (180 - L)
A = 180 L - L²
differentiate with respect to L.
dA / dL = 180 - 2 L
Put it equal to zero for maxima and minima
180 - 2L = 0
L = 90 feet
W = 180 - 90 = 90 feet
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