Question 138952
Short side: a
Longest side: c (the hypotenuse)
Medium side: b


Since it is a right triangle:


{{{c^2=a^2+b^2}}}


But {{{c=3a+4}}}, and {{{b=2a+10}}}


So:
{{{(3a+4)^2=a^2+(2a+10)^2}}}


Expand the binomials, collect like terms on the left, set the whole thing equal to zero, and then solve the quadratic.  Hint: the quadratic factors, but factor out a 4 before you start looking for the binomial factors.  Hint: One of your roots will be negative, exclude it because you are looking for a positive measure of length.