SOLUTION: I need help solving this problem....the sides of a right triangle are x, x+1 and x+2 units long. Find the side lengths of the triangle by solving for x.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help solving this problem....the sides of a right triangle are x, x+1 and x+2 units long. Find the side lengths of the triangle by solving for x.      Log On


   

Question 607241: I need help solving this problem....the sides of a right triangle are x, x+1 and x+2 units long. Find the side lengths of the triangle by solving for x.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Since it is a right triangle, you can employ the Pythagorean theorem to solve for x: c%5E2+=+a%5E2%2Bb%5E2 and the longest side (the hypotenuse) is x+2
%28x%2B2%29%5E2+=+%28x%2B1%29%5E2%2Bx%5E2 Simplify.
%28x%5E2%2B4x%2B4%29+=+%28x%5E2%2B2x%2B1%29%2Bx%5E2 Combine like-terms.
x%5E2%2B4x%2B4+=+2x%5E2%2B2x%2B1 Subtract x%5E2 from both sides.
4x%2B4+=+x%5E2%2B2x%2B1 Subtract 4x from both sides.
4+=+x%5E2-2x%2B1 Subtracr 4 from both sides.
0+=+x%5E2-2x-3 Factor this trinomial.
%28x%2B1%29%28x-3%29+=+0 Apply the zero product rule.
x%2B1+=+0 or x-3+=+0 so...
x+=+-1 or x+=+3 Discard the negative solution.
x+=+3, x%2B2+=+5, and x%2B1+=+4