SOLUTION: i was never taught this and i don't know how to solve something like this, could you please help?? a right triangle has legs x+1. The hypotenuse of the triangle is 2x-1. What i

Question 187798: i was never taught this and i don't know how to solve something like this, could you please help??
a right triangle has legs 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 both legs are 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.

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 .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

or Reduce

So the answers are or

which approximate to or

Since generates a negative length, we'll ignore this answer.

So the only solution is

This means that the two legs are

And the hypotenuse is

================================================================

Answer:

So the legs are approximately 5.121 units long and the hypotenuse is about 7.242 units long

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