SOLUTION: Prove that if m is a real number and m, m +1, and m +2 are the lengths of the three sides of a right triangle, then m=3. Please help.

Question 536989: Prove that if m is a real number and m, m +1, and m +2 are the lengths of the three sides of a right triangle, then m=3.
Please help.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If m, m+1 and m+2 are the length of the sides of a right triangle,
they are all positive numbers and
the length of the hypotenuse is the largest number, m+2.
Then Pythagoras theorem says
-->--> -->
The solutions of the equation are and ,
but since m must be positive, the only solution is .
The triangle is a 3-4-5 triangle, corresponding to the best known of the Pythagorean triples (sets of 3 positive integers that can be sides of a right triangle).

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