# 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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