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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