SOLUTION: A right triangle has legs x and x+1. The hypotenuse of the triangle is 2x-1. What is the length of the hypotenuse?

Question 187808: A right triangle has legs x and x+1. The hypotenuse of the triangle is 2x-1. What is the length of the hypotenuse?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We basically have this triangle set up:

Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , , and

FOIL

Combine like terms.

Get all terms to the left side.

Combine like terms.

Factor the left side.

or Set each factor equal to zero

or Solve for "x" in each case

Ignoring the trivial solution , the only answer is

So the leg "x" is 3 units long

The leg is 3+1=4 units long

and the hypotenuse is 2(3)-1=6-1=5 units long

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Answer:

So the legs are 3 and 4 units long while the hypotenuse is 5 units long.

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