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    Heron's formula and Pythagoras

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    Begin with a right triangle with sides: a, b, and hypotenuse c.
    Determine the area two ways:
    Heron's Formula & A = (½)ab
    Equate and manipulate these equations to end up with the Pythagorean Theorem.

    i) Let the sides of a triangle have lengths a, b, and c. The semiperimeter is p = (a + b + c) / 2 and let A be the area. Heron's ...

    Solution Summary

    This problem relates Heron's formula with the Pythagorean theorem.