SOLUTION: The Pythagorean Theorem for right triangles states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a^2 + b^2= c^2.

Algebra ->  Geometry-proofs -> SOLUTION: The Pythagorean Theorem for right triangles states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a^2 + b^2= c^2.       Log On


   

Question 494477: The Pythagorean Theorem for right triangles states that if a and b are the
lengths of the legs of a right triangle and c is the length of the hypotenuse,
then a^2 + b^2= c^2.
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.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28m%2B2%29%5E2+=+m%5E2+%2B+%28m%2B1%29%5E2
m%5E2%2B4m%2B4+=+m%5E2+%2B+m%5E2%2B2m%2B1
4m%2B4+=+m%5E2+%2B+2m+%2B+1
m%5E2+-+2m+-+3+=+0
(m-3)*(m+1) = 0
m = -1 Ignore
m = 3
--> The 3, 4, 5 right triangle