Help. ​

Triangle HTM  is similar to triangle MTA ....so....

HT/TM  = TM/TA     and TA  = x   ....so...

12/5 = 5/x

12x = 25

x = 25/12

And

HT/HM  = MT/ MA      and MA  = y.....so....

12/13  = 5/y     cross-multiply

12y = 13*5

12y = 65

y = 65 / 12

Help.

Geometric mean theorem:

$\begin{array}{|rcll|} \hline 5^2 &=& 12\cdot x \\ x &=& \frac{25}{12} \\ \hline \end{array}$

Cathetus Theorem:

$\begin{array}{|rcll|} \hline y^2 &=& x\cdot (x+12) \\ y^2 &=& \frac{25}{12}\cdot (\frac{25}{12}+12) \\ y^2 &=& \frac{25}{12}\cdot (\frac{25+144}{12}) \\ y^2 &=& \frac{25}{12}\cdot (\frac{169}{12}) \\ y^2 &=& \frac{5^2}{12^2}\cdot 13^2 \\ y &=& \frac{5 }{12 }\cdot 13 \\ y &=& \frac{65}{12 }\\ \hline \end{array}$