Mathematics, 23.12.2020 03:50 roorootx

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

In the accompanying diagram. altitude CD is

drawn to the hypotenuse of right triangle ABC. If
AD

Answers

Answer from: ezzyandrade7

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 .

Answer from: Quest

12 rio aoice of q kqpd so r lagr

Answer from: Quest

The answer is 4 points

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In the accompanying diagram. altitude CD is drawn to the hypotenuse of right triangle ABC. If