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NotTheSmartest  Mar 9, 2017
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 #1
avatar+76802 
+5

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

 

 

 

cool cool cool

CPhill  Mar 9, 2017
 #2
avatar+18599 
0

Help.

Geometric mean theorem:

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

 

Cathetus Theorem:

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

 

laugh

heureka  Mar 10, 2017

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