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Math Help - Getting min. value of this problem.

  1. #1
    hakuoro07
    Guest

    Getting min. value of this problem.

    I'm confused with this problem:

    What should be the shape of a rectangular field of a given area if it is enclosed by the least amount of fencing? Explain.

    I know it's supposed to be rectangle, but I don't know how to create and equation that will explain it.

    Someone pls. help.
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  2. #2
    MHF Contributor
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    Rule #1 - Name Stuff

    It's a rectangle.

    L = Length > 0
    W = Width > 0

    Rule #2 - Dump Information from Your Brain

    Perimeter(L,W) = 2*L + 2*W > 0

    Area(L,W) = L*W > 0

    If anything else ABOUT RECTANGLES comes to mind, write it down, too.

    Rule #3 Search for clues.

    "field of a given area" -- Aha! Here is a parameter that doesn't move around. This gives:

    L = Area/W (Or W = Area/L if you like. I'll use the first.)

    and

    Perimeter(W) = 2*(Area/W) + 2*W

    I suspect you can now minimize Perimeter(W) with respect to the single variable "W".

    Finally, you must ask how W relates to L. This is the exciting part of the problem!
    Last edited by TKHunny; March 17th 2008 at 09:37 AM. Reason: Typo
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