SOLUTION: Please help me solve this equation. i can not solve this question for my homework it said: The sides of the right-angle triangle are x,[x+2]and[2x-2]. The hypotenuse is lenght[2

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Question 717127: Please help me solve this equation.
i can not solve this question for my homework
it said:
The sides of the right-angle triangle are x,[x+2]and[2x-2]. The hypotenuse is lenght[2x-2]. Find the actual dimensions of the triangle.
My math teacher told me to use Pythagoras Theorem c^2 = a^2+b^2 but i not sure about that.
Thank you for your help.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Do exactly what your teacher told you to do. If the hypotenuse is , then we can say . The designation as to the other two sides is arbitrary because of the commutativity of addition, so we can assign and . Now plug these values into the Pythagorean relationship:

Now all you have to do is expand the squared binomials and collect like terms in the LHS. That will leave you with a quadratic expression equal to zero, which is simply a quadratic equation. Given correct arithmetic you will have an easily factorable quadratic equation. Discard the zero root because that is clearly absurd, leaving you with a positive integer value for that you can use to calculate the measures of your three triangle sides.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it