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Math

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If Steve has 120 feet of fence to make a rectangular kennel and he will use his house on one side, how would the dimensions be found for a kennel with the greatest area be found?

  • Math - ,

    L + 2 w = 120
    A = L w
    A = (120 -2w)w = 120 w - 2 w^2
    that is parabola opening down, find the vertex (I assume you do not know calculus which would be easier)
    -2 w^2 + 120 w = A
    complete square
    w^2 - 60 w = -A/2
    w^2 - 60 w + 30^2 = -A/2 + 900
    (w-30)^2 = -A/2 + 900
    so
    w = 30
    then L = 120 - 60 = 60

  • Math - ,

    Area= LW
    Perimeter= 2L+ W

    dArea/dL= W + dW/dl

    the last term you get from taking the derivative of the perimeter equation
    0 (perimeter is constant)=2 + dW/dl

    so put that in the darea/dl, set to zero, and solve for W.

  • Math - ,

    Thanks

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