SOLUTION: the length of one leg of a right triangle is 7 meters less than the length of the other leg. the length of the hypotenuse is 13 meters. find the lengths of the legs.

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Question 181935: the length of one leg of a right triangle is 7 meters less than the length of the other leg. the length of the hypotenuse is 13 meters. find the lengths of the legs.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

We basically have this triangle set up:





Since the legs are and this means that and


Also, since the hypotenuse is , this means that .


Start with the Pythagorean theorem.


Plug in , ,


Square to get .


FOIL


Subtract 169 from both sides.


Combine like terms.




Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the possible answers are or


However, a negative length is NOT possible. So is NOT a solution


So the only answer is





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Answer:


So the solution is


This means that the other leg is


So the two legs are: 12 and 5 units

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