Posted by **Barb** on Saturday, February 2, 2013 at 3:12am.

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

- Math--Please help -
**Reiny**, Saturday, February 2, 2013 at 8:59am
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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