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.

Algebra ->  Triangles -> 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.       Log On


   

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) About Me  (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
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
The solutions of the equation are m=-1 and m=3,
but since m must be positive, the only solution is m=3.
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).