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Math Help - Find all such triangles for this to be possible.

  1. #1
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    Find all such triangles for this to be possible.

    Ethan is trying to find the area of a triangle, but he only has its side lengths and does not know Heron's formula. Mistakenly, he decides to multiply the side lengths together (similar to how he would find the area of a rectangle) to find its area. Miraculously, Ethan computes the correct area!

    Find all triangles for which this is possible.
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  2. #2
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    If ABC is circumscribed in a circle with radius R
    A=\frac {abc}{4R}

    abc=\frac {abc}{4R}

     4Rabc=abc
     4R=1
     R=\frac {1}{4}

    So for every triangle with R=1/4 A=abc
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