SOLUTION: The sides of a right triangle are consecutive multiples of three. Find the length of the hypotenuse.

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Question 324637: The sides of a right triangle are consecutive multiples of three. Find the length of the hypotenuse.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem,
A%5E2%2BB%5E2=C%5E2
%283n%29%5E2%2B%283%28n%2B1%29%29%5E2=%283%28n%2B2%29%29%5E2
9n%5E2%2B9%28n%2B1%29%5E2=9%28n%2B2%29%5E2
n%5E2%2B%28n%5E2%2B2n%2B1%29=n%5E2%2B4n%2B4
2n%5E2%2B2n%2B1=n%5E2%2B4n%2B4
n%5E2-2n-3=0
%28n%2B1%29%28n-3%29=0
Two solutions:
n%2B1=0
n=-1
A negative length doesn't make sense in this problem.
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n-3=0
n=3
(9,12,15)
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15 is the length of the hypotenuse.