SOLUTION: The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches longer than the remaining side. Find the dimensions of the triangle

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Question 61668: The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches longer than the remaining side. Find the dimensions of the triangle
Answer by joyofmath(189) About Me  (Show Source):
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The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches longer than the remaining side. Find the dimensions of the triangle
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Let S be the short side of the triangle.
Then S+6 is the hypotenuse.
And, the remaining side is S+3 because it's 3 inches shorter than the hypotenuse.
So, using the Pythagorean Theorem: S%5E2%2B%28S%2B3%29%5E2+=+%28S%2B6%29%5E2.
Square everything and we get S%5E2+%2B+S%5E2%2B6S%2B9+=+S%5E2%2B12S%2B36
or 2S%5E2%2B6S%2B9+=+S%5E2%2B12S%2B36.
Subtract S%5E2 from both sides: S%5E2%2B6S%2B9+=+12S%2B36.
Subtract 12S from both sides: S%5E2-6S%2B9+=+36.
Subtract 36 from both sides: S%5E2-6S-27+=+0.
This factors into %28S-9%29%28S%2B3%29+=+0+.
So, S=9 or S=-3. But, S can't be negative, so S=9.
Verify that S=9 is correct.
S%5E2%2B%28S%2B3%29%5E2+=+9%5E2+%2B+12%5E12+=+81+%2B+144+=+225 which is indeed 15%5E2.