Question

In the given figure, ∠ABC = 90° and BD⊥AC. If BD = 8cm, AD = 4cm, find CD.

Answer 1

It is given that ABC is a right angled triangle 

and BD is the altitude drawn from the right angle to the hypotenuse. 

In ∆ DBA and ∆ DCB, we have : 

∠BDA = ∠CDB

∠DBA = ∠DCB = 90°

Therefore, by AA similarity theorem, we get : 

∆DBA - ∆ DCB 

⇒ BD/CD = AD/BD

⇒ CD = BD^2/AD 

CD = 8×8/4 = 16 cm