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 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!
RELATED QUESTIONS
The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches (answered by joyofmath)
The hypotenuse of a right triangle is 16 inches longer than the shortest side and 8... (answered by ankor@dixie-net.com)
The hypotenuse of a right triangle is 10 inches longer than the shortest side and 5... (answered by jorel1380)
The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in.... (answered by mananth,stanbon)
Hypotoneuse Headaches! Please help me! I cannot figure these out. Been wrong 4 times... (answered by Alan3354,scott8148)
The hypotenuse of a right triangle is 4 cm longer than the shortest side and 2 cm longer... (answered by stanbon,jorel1380,chriswen)
The hypotenuse of a right triangle is 12cm longer than the shortest side, and 6cm longer... (answered by macston)
The shortest side of a triangle is three inches shorter than the longest side. The... (answered by Fombitz)
A right triangle has a height that is 6 inches longer than its shorter side. The... (answered by macston)