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

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) (Show Source): You can put this solution on YOUR website!
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: .
Square everything and we get
or .
Subtract from both sides: .
Subtract 12S from both sides: .
Subtract 36 from both sides: .
This factors into .
So, or . But, S can't be negative, so .
Verify that is correct.
which is indeed .
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