Question

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.

Answer 1

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 = 8.1 cm