A town decides to build a playground using one of the existing walls beside an elementary school. What is the maximum area they can enclose using only 100ft of donated fence?

Answer 1

Letting L be the length against the building,

100 = L + 2W
so, L = 100-2W

A = WL = W(100-2W)
= 100W - 2W^2

This has a max at W = 100/4 = 25
L = 50

A = 25*50 = 1250 ft^2

Answer 2

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