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My proof involving Pythagorean’s Theorem

  1. Feb 27, 2010 #1

    1. The problem statement, all variables and given/known data

    Let a, b, and c be lengths of sides of triangle T, where a ≤ b ≤ c.
    Prove that if T is a right triangle, then (abc)2=(c6-a6-b6)/3

    2. Relevant equations

    If T is a right triangle, then Pythagorean’s Theorem states:
    The sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse. That is a2+b2=c2, where c is the hypotenuse.

    3. The attempt at a solution

    We assume the given equation and using Pythagorean’s Theorem, we obtain solutions for c2 and c6:
    We substitute these results into the original equation.
    This produces an equation where the left hand side is identical to the right hand side.
    Since these terms are equal, it follows that the original equation holds true for a right triangle.

    This is what I have. I am curious to if the proof is correct/acceptable.

    Thanks for any feedback.
    Last edited: Feb 27, 2010
  2. jcsd
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