Question 132345: I need some help on this problem please: find out the length of sides a & b on the following triangle. A=x, b=3x and c = 19. I think I should use the pythagorean theorem. I squared 19 to get 361, but I don't know how to figure the rest. Any advice would be great.
Found 2 solutions by solver91311, checkley71:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! You don't say, and I certainly can't see the figure, but I'll just assume that you have a right triangle and that side c is the hypotenuse. Given those assumptions, the Pythagorean Theorem is the correct approach to the solution.
We know that  , so let's substitute the given values and see where it takes us.
 is certainly an answer to the problem, but it is not in simplest terms because of the radical in the denominator. Simplest terms demands that, if possible, the denominator must be a rational number.
So, we need to perform a process called rationalizing the denominator. In this case, all we need to do is multiply by  in the form of 
 . Final answer, Regis.
Answer by checkley71(8403)  (Show Source):
You can put this solution on YOUR website! IF YOU HAVE A RIGHT TRIANGLE AND THE 19 SIDE IS THE HYPOTENUSE THEN YES USE THE PYTHAGOREN THERUM:
X^2+(3X)^2=19^2
X^2+9X^2=361
10X^2=361
X^2=361/10
X=SQRT36.1
X=6.008 ANSWER FIOR THE SHORTER SIDE.
X=3*6008
X=18.025 ANSWER FOR THE LONGER SIDE.
PROOF
6.008^2+18.025^2=19^2
36+325=361
361=361
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