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.

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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