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Math Help - cut a wire and make some shapes

  1. #1
    Super Member angel.white's Avatar
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    cut a wire and make some shapes

    So you have a wire that is 10 meters long, you want to cut it at some point, and use one section to make a square, and the other section to make an equilatteral triangle. What lengths should you cut the wire into in order to have the greatest area when combining the areas of square and the triangle.

    I got that the triangle should be from a wire lengthed approximately 5.650 meters, and the square should be from 4.349 meters.

    If someone could verify this for me, I would really appreciate it.
    Last edited by angel.white; November 16th 2007 at 02:08 PM.
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  2. #2
    Senior Member Peritus's Avatar
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    I've checked it and I get the same result.
    triangle wire length = y
    square wire length = x

    Ssquare = (x/4)^2
    Striangle = (sqrt(3)/36)*y^2

    Stotal = (x/4)^2 + (sqrt(3)/36)*y^2

    subject to x+y = 10

    I've plugged in x = 10-y ,and took the derivative of Stotal with respect to y...
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by Peritus View Post
    I've checked it and I get the same result.
    triangle wire length = y
    square wire length = x

    Ssquare = (x/4)^2
    Striangle = (sqrt(3)/36)*y^2

    Stotal = (x/4)^2 + (sqrt(3)/36)*y^2

    subject to x+y = 10

    I've plugged in x = 10-y ,and took the derivative of Stotal with respect to y...
    Thank you, I appreciate it.
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  4. #4
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    Hello, angel.white!

    I got the same answers . . . Nice work!

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