Q8 of 186 Page 211

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.

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.


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