SOLUTION: if one leg of a triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs.

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Question 156845: if one leg of a triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Leg 1:


Leg 2: (since one leg is 14 m shorter than the other, the other leg is 14 m longer than the first one)


Hypotenuse: 26



Start with Pythagorean's Theorem


Plug in the given information


Square 26


FOIL


Combine like terms


Subtract 676 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


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 isn't possible. So the only answer is


So the first leg is 10 m, the second leg is 24 m (since ), and the hypotenuse is 26 m


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