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Math Help - Quadratic Story Problem

  1. #1
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    Quadratic Story Problem

    Question:
    A Building contractor wants to fence in a rectangular plot adjacent to a strait highway using the highway for one side, which will be left unfenced. If the contractor has 500 ft of fence , find the dimensions of the maximum enclosed area.

    I know the answer to this question is 125x250, but I have no idea how they got that. It doesn't seem like there is enough information without assuming that the rectangle's sides are A x 2A x A x 2A(the last side not fenced). Should I be assuming this? How should I set up this problem?
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  2. #2
    Senior Member MacstersUndead's Avatar
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    A rectangular plot need not have A x 2A x A x 2A

    You know the perimeter = 500 and that area = MAX

    so,
    2a + b = 500
    and
    ab = MAX

    use substitution and you get a quadratic where the MAX is the value at the vertex of the downward parabola.
    Last edited by MacstersUndead; September 27th 2009 at 09:29 PM.
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