Q23 of 95 Page 6

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: ABC = 90° and BD AC

and AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm


To find: BC


Firstly, we have to show that ABC ~BDC


Let ABC and BDC


∠ABC = ∠BDC [each 90°]


∠ACB = ∠BCD [common angle]


∴ ABC ~BDC [by AA similarity criterion]


Since, triangles are similar, hence corresponding sides are proportional.





⇒ BC = 8.1cm


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