SOLUTION: The hypotenuse of a right triangle is 5 inches. The lengths of the two legs are given by two consecutive integers. Find the lengths of the two legs.

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Question 225108: The hypotenuse of a right triangle is 5 inches. The lengths of the two legs are given by two consecutive integers. Find the lengths of the two legs.
Found 2 solutions by rfer, Earlsdon:
Answer by rfer(12662) About Me  (Show Source):
You can put this solution on YOUR website!
This is a triple
A good ole 3, 4, 5 triangle

Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two legs be x and x+1, then from the Pythagorean theorem, we have:
x%5E2%2B%28x%2B1%29%5E2+=+5%5E2
x%5E2%2B%28x%5E2%2B2x%2B1%29+=+25
2x%5E2%2B2x%2B1+=+25 Subtract 25 from both sides.
2x%5E2%2B2x-24+=+0 Factor out a 2.
2%28x%5E2%2Bx-12%29+=+0 so...
x%5E2%2Bx-12+=+0 Factor this quadratic equation.
%28x%2B4%29%28x-3%29+=+0 and...
x+=+-4 or x+=+3 Discard the negative solution as lengths are positive.
x+=+3 and x%2B1+=+4
The two legs are 3 inches and 4 inches.