document.write( "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.
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Algebra.Com's Answer #352706 by KMST(5328) $\"\"$ $\"About$

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If m, m+1 and m+2 are the length of the sides of a right triangle,
\n" ); document.write( "they are all positive numbers and
\n" ); document.write( "the length of the hypotenuse is the largest number, m+2.
\n" ); document.write( "Then Pythagoras theorem says
\n" ); document.write( " $\"m%5E2%2B%28m%2B1%29%5E2=%28m%2B2%29%5E2\"$ --> $\"2m%5E2%2B2m%2B1=m%5E2%2B4m%2B4\"$ --> $\"m%5E2-2m-3=0\"$ --> $\"%28m%2B1%29%28m-3%29=0\"$
\n" ); document.write( "The solutions of the equation are $\"m=-1\"$ and $\"m=3\"$ ,
\n" ); document.write( "but since m must be positive, the only solution is $\"m=3\"$ .
\n" ); document.write( "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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