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Math Help - Triangle Optimization

  1. #1
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    Triangle Optimization

    Hello:

    I am presented with a problem in which I must maximize the area of a triangle with a perimeter of 12.

    I do not necessarily want an answer with the numbers I provided, but rather the general step by step methodology in terms of how this problem is done.
    Thanks so much, I am a bit lost as to how to optimize in the first place!
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  2. #2
    Senior Member
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    Mar 2010
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    The area of triangle is
    S^2=s(s-x)(s-y)(s-z)
    12=x+y+z
    s=12/2=6
    or
    S^2=6(6-x)(6-y)(6-z)=6(y+z-6)(6-y)(6-z)
    find max S with y and z.
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  3. #3
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    Apr 2010
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    Thanks! I really appreciate the help.. One last, quick thing.
    The problem in question asks us to find the maximum area of a V shaped object with a perimeter of 12. The top of the V however, is not factored into the total perimeter (meaning each side of the V shape is 6 in length)
    Does this change the calculation in any particular way? Should I "make up" an additional length for the open side in question and then subtract it out of my optimization equation in the end?
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