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Algebra

A homeowner wants to fence a rectangular garden using 60 ft of fencing. An existing stone wall will be
used as one side of the rectangle. Find the dimensions for which the area is a maximum

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Willia

  1. 60 = L + 2 w so L = 60 -2 w

    A = L w
    A = (60-2 w)w = 60 w - 2 w^2

    If you know calculus, just take derivative and set to zero and you are done
    If not, complete the square to find vertex of parabola.

    w^2 - 30 w = -A/2
    w^2 - 30 w + 225 = -A/2 + 225
    (w-15)^2 = -(1/2)(A - 450)
    so
    w = 15
    L = 60 - 30 = 30
    area = 450 by the way

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    Damon

  2. So the maximum area would be 450?
    I'm trying to read through your work so I can understand how you got the answer

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    Willia

  4. Nope I still don't get it. I understand right up until this...
    "
    w^2 - 30 w = -A/2
    w^2 - 30 w + 225 = -A/2 + 225
    (w-15)^2 = -(1/2)(A - 450)
    so
    w = 15
    L = 60 - 30 = 30
    area = 450 by the way
    "
    Thanks anyway!

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    Willia

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