To Find :
The value of side CD.
Solution :
Applying Pythagoras theorem in ΔABC :
[tex]AC^2 + CB^2=AB^2 \\\\AC^2 + CB^2 = 13^2[/tex] ....1)
Applying Pythagoras theorem in ΔACD and ΔCDB :
[tex]AD^2 + CD^2 = AC^2[/tex] ....2)
[tex]CD^2 + DB^2 = CB^2[/tex] ....3)
Adding equation 2 and 3, we get :
[tex]AC^2 + CB^2 =AD^2 + 2CD^2 + DB^2[/tex] ...4)
Solving equation 1) and 4), we get :
[tex]AD^2 + 2CD^2 + DB^2 = 13^2\\\\9^2 + 2CD^2 + ( 13 - 9 )^2 = 13^2\\\\2CD^2 = 72\\\\CD = 6[/tex]
Therefore, length of CD is 6 .
