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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:




Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are x and x%2B1 this means that a=x and b=x%2B1


Also, since the hypotenuse is 2x-1, this means that c=2x-1.



a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B%28x%2B1%29%5E2=%282x-1%29%5E2 Plug in a=x%2B1, b=x%2B1, and c=2x-1


x%5E2%2Bx%5E2%2B2x%2B1=4x%5E2-4x%2B1 FOIL


2x%5E2%2B2x%2B1=4x%5E2-4x%2B1 Combine like terms.


2x%5E2%2B2x%2B1-4x%5E2%2B4x-1=0 Get all terms to the left side.


-2x%5E2%2B6x=0 Combine like terms.


-2x%28x-3%29=0 Factor the left side.


-2x=0 or x-3=0 Set each factor equal to zero


x=0 or x=3 Solve for "x" in each case


Ignoring the trivial solution x=0, the only answer is x=3


So the leg "x" is 3 units long

The leg x%2B1 is 3+1=4 units long

and the hypotenuse 2x-1 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.