Given that, ∠ABC = 90°

AD = 4 cm

BD = 8 cm

In order to find CD, we need to prove that ∆BDC and ∆ABC are similar.

∠BDC = ∠ADB = 90°

∠DBA = ∠DCB

We have proved ∆DBA ∼ ∆DCB, by AA-similarity criteria.

So we can write,

⇒

⇒

⇒ CD = 16

Hence, CD = 16 cm.