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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

  • math -

    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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