+129899 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
+26393 Help.
Geometric mean theorem:
\(\begin{array}{|rcll|} \hline 5^2 &=& 12\cdot x \\ x &=& \frac{25}{12} \\ \hline \end{array}\)
Cathetus Theorem:
\(\begin{array}{|rcll|} \hline y^2 &=& x\cdot (x+12) \\ y^2 &=& \frac{25}{12}\cdot (\frac{25}{12}+12) \\ y^2 &=& \frac{25}{12}\cdot (\frac{25+144}{12}) \\ y^2 &=& \frac{25}{12}\cdot (\frac{169}{12}) \\ y^2 &=& \frac{5^2}{12^2}\cdot 13^2 \\ y &=& \frac{5 }{12 }\cdot 13 \\ y &=& \frac{65}{12 }\\ \hline \end{array}\)
