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 133099: 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.
Found 2 solutions by checkley71, vleith:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
X^2+(X+3)^2=(X+6)^2
X^2+X^2+6X+9=X^2+12X+36
X^2-6X-27=0
(X-9)(X+3)=0
X-9=0
X=9 ANSWER FOR THE SHORTEST SIDE.
9+3=12 FOR THE LONGER SIDE
9+6=15 FOR THE HYPOTENUSE.
PROOF:
9^2+12^2=15^2
81+144=225
225=225

Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
Let the shortest side = s. Then the hypotenuse is (s+6) and the other side is (s+6)-3 = (s+3)
Using the Pythagorean theorem,
So:

collecting terms yields:

Thus s = 9 (since it can't be a length of -3)
Then the other 2 kegs are (s+3) = 12 and (s+6) = 15
Check your answer.
Is 9^2 + 12^2 = 15^2? yes it is!