Question

In the accompanying diagram. altitude CD is

drawn to the hypotenuse of right triangle ABC. If
AD - 9 and AB = 13. find CD.

Someone help me please

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 .