Math, Quadratics

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Farmer John is building a pen to keep his pig in. John has 40m of fencing. He will only need to make 3 sides to the pen because the 4th side will be along a barn. If John wants the maximum area what should the side lengths of the pen be?

  • Math, Quadratics -

    L + 2w = 40
    so
    L = 40 - 2w

    A = L * w
    A =(40-2 w)(w) = 40 w - 2 w^2

    2 w^2 - 40 w = -A
    w^2 - 20 w = -A/2

    w^2 - 20 W + 100 = -A/2 + 100
    (w-10)^2 = -(1/2)(A-200)
    vertex at w = 10, A = 200
    so L = 20

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