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Ex. 120 m of fencing is to be used to form three sides of a rectangular enclosure , the fourth side being an existing wall . Find the maximum possible area of the enclosure

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L + 2 W = 120 so L = 120 - 2 W
A = L W
A = (120-2W)W = 120 W - 2 W^2

so
2 W^2 -120 W = - A

W^2 - 60 W = -A/2

W^2 - 60 W + 900 = -A/2 + 900

(W-30)^2 = -(1/2)(A-1800)

vertax of parabola at (30,1800)

so
W = 30
L = 120 - 60 = 60
and A = 1800 m^2

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