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Math Help - Triangle optimization

  1. #1
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    Oct 2009
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    Triangle optimization

    An isoceles triangle has its vertex at the origin and its base parallel to the x-axis with the vertices above the axis on the curve y = -x^2 + 27. What is the largest area the triangle can have?

    I know what the picture looks like, but that's about it..
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    319
    We may use the triangle area formula

    A=\frac{1}{2}bh=\frac{1}{2}\cdot 2x\cdot (27-x^2)\;\;\;\;\;\;\;\;\;\;\; 0\le x\le 3\sqrt{3}

    together with the symmetry of the graph of y=27-x^2.
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