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Math--Please help

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Prove that no isosceles right triangle exists whose sides are integers.

  • Math--Please help - ,

    let the shorter sides be x units each ,
    let the hypotenuse be h
    (clearly we can't have the equal sides being the hyppotenuses, or else we would have 2 right angles, leaving nothing left for the third angle)

    h^2 = x^2 + x^2
    h^2 = 2x^2
    h = √2x
    so whatever integer x is, multiplying an integer by √ makes it irrational, thus no longer an integer.

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