Question

In the accompanying diagram. altitude CD is

Answer 1

To Find :

The value of side CD.

Solution :

Applying Pythagoras theorem in ΔABC :

$AC^2 + CB^2=AB^2 \\\\AC^2 + CB^2 = 13^2$     ....1)

Applying Pythagoras theorem in ΔACD and ΔCDB :

$AD^2 + CD^2 = AC^2$     ....2)

$CD^2 + DB^2 = CB^2$     ....3)

Adding equation 2 and 3, we get :

$AC^2 + CB^2 =AD^2 + 2CD^2 + DB^2$   ...4)

Solving equation 1) and 4), we get :

$AD^2 + 2CD^2 + DB^2 = 13^2\\\\9^2 + 2CD^2 + ( 13 - 9 )^2 = 13^2\\\\2CD^2 = 72\\\\CD = 6$

Therefore, length of CD is 6 .