Question

In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, 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 Δ DBA and Δ DCB, we have : 

∠𝐵𝐷𝐴= ∠𝐶𝐷𝐵
∠𝐷𝐵𝐴= ∠𝐷𝐶𝐵=90°
Therefore, by AA similarity theorem, we get :
ΔDBA - Δ DCB 

⇒ `(BD)/(CD)=(AD)/(BD)` 

⇒ `CD=(BD^2)/(AD)` 

`CD = (8xx8)/4=16  cm`