In the given figure, ∠ ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Question

Philoid · Accepted Answer

Given that, ∠ABC = 90°

AB = 5.7 cm

BD = 3.8 cm

CD = 5.4 cm

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

∠BDC = ∠ABC = 90°

∠ACB = ∠DCB [They are common angles]

By this we have proved ∆BDC ∼ ∆ABC, by AA-similarity criteria.

So we can write,

⇒

⇒ BC = 8.1

Hence, BC = 8.1 cm.

In the given figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.