SOLUTION: The lengths of the legs of a right triangle are y and (3y-1)m and the hypotenuse is (3y+1)m, find y

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Question 1146004: The lengths of the legs of a right triangle are y and (3y-1)m and the hypotenuse is (3y+1)m, find y
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
By the Pythagorean theorem,

y%5E2%2B%28%283y-1%29m%5E%22%22%29%5E2=%28%283y%2B1%29m%5E%22%22%29%5E2

y%5E2=%283y%2B1%29%5E2m%5E2-%283y-1%29%5E2m%5E2

Factor out m² on the right side:

y%5E2=%28%283y%2B1%29%5E2-%283y-1%29%5E2%29m%5E2

The factor in parentheses on the right side factors 
as the difference of squares:

y%5E2=%28%283y%2B1%29-%283y-1%29%5E%22%22%29%28%283y%2B1%29%2B%283y-1%29%5E%22%22%29m%5E2%29

y%5E2=%283y%2B1-3y%2B1%5E%22%22%29%283y%2B1%2B3y-1%5E%22%22%29m%5E2%29

y%5E2=%282%5E%22%22%29%286y%5E%22%22%29m%5E2%29

y%5E2=12ym%5E2%29

All sides of a triangle must be positive so y > 0,
and we may divide both sides by y

y=12m%5E2%29

Edwin