Question 921845
The original triangle analyzed:
Let x be some positive real number.
USING Pythagorean Theorem formula,  {{{(5x)^2+(6x)^2=(2sqrt(61))^2}}}, and you can solve this for x.


STEPS TO FIND x.
{{{25x^2+36x^2=2*2*61}}}
{{{61x^2=4*61}}}
{{{x^2=4}}}
{{{highlight(x=2)}}}


The next part gives new conditions and a question.

The original triangle's legs are  {{{5*2=10}}}, and {{{6*2=12}}}.


The side 12 is to be doubled, meaning becomes 24; and the side 10 remains unchanged.  Find the new hypotenuse!