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Math Help - largest area geometry

  1. #1
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    largest area geometry

    I got this assignment tomorrow and am having trouble.
    "If you have 100 meters of fence, what are the dimensions of the maximum area you can enclose?"

    "Also, if you want to enclose 100 square meters of land what is the maximum length of fence you can use?"
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  2. #2
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    Quote Originally Posted by AndrewT View Post
    ...

    "If you have 100 meters of fence, what are the dimensions of the maximum area you can enclose?"
    The area with a minimum circumference is a circle. Thus the maximum area with a circumference of 100 m is a circle with a diameter of 31.83 m and the value of the area is 795.775 mē

    "Also, if you want to enclose 100 square meters of land what is the maximum length of fence you can use?"
    There doesn't exist a maximum length of the fence. If the area is a rectangle then you can calculate the length with respect to the width of the rectangle:

    l=\frac{100}{w}

    If w is becoming smaller and smaller l is growing more and more. In the end you need a fence of infinite length to enclose nothing.
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  3. #3
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    Thanks man you are a life saver.

    P.S you are really smart I could probably never figure thathttp://www.mathhelpforum.com/math-he...9-headbang.gif
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  4. #4
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    Quote Originally Posted by earboth View Post
    The area with a minimum circumference is a circle.

    [snip]
    A more interesting question is proving this. I'm happy to give a proof if there's an expression of interest.
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    A more interesting question is proving this. I'm happy to give a proof if there's an expression of interest.
    5.5% VAT.

    Or \rm{interest}=\frac{\text{attention}}{\textrm{time  }}

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