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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