Question 326202: The hypotenuse of a right triangle is 1 cm longer than the longer leg. The shorter leg is 7 cm shorter than the longer leg. Fin the length of the longer leg of the triangle
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Right triangle? Look to  , that's Mister Pythagoras to you.
Let  represent the long leg. Then the hypotenuse is  and the short leg is  . Hmm, this is beginning to look like a 5-12-13 triangle...
Pythagoras says:
^2\ =\ x^2\ +\ (x\ -\ 7)^2)
Multiply it all out and gather like terms (verification left as an exercise for the student):
Factor:
(x\ -\ 12)\ =\ 0)
So,  or 
But if , meaning the long leg is 4, and we subtract 7 to get the short leg, you end up with a short leg that is -3. That makes no sense, so the only valid answer is that the long leg is 12, the short leg is 7 less than that or 5, and the hypotenuse is one more, i.e. 13.
John
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