Question 132345
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 {{{a^2+b^2=c^2}}}, so let's substitute the given values and see where it takes us.


{{{x^2+(3x)^2=19^2}}}


{{{x^2+9x^2=19^2}}}


{{{10x^2=19^2}}}


{{{x^2=19^2/10}}}


{{{x=sqrt(19^2/10)=sqrt(19^2)/sqrt(10)=19/sqrt(10)}}}


{{{19/sqrt(10)}}} 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 {{{19/sqrt(10)}}} by {{{1}}} in the form of {{{sqrt(10)/sqrt(10)}}}


{{{(19/sqrt(10))(sqrt(10)/sqrt(10))=19sqrt(10)/10}}}.  Final answer, Regis.