Question

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

Answer 1

We have, ∠ABC = 90° and BD ⊥ AC

In ΔABC and ΔBDC

∠ABC = ∠BDC                     [Each 90°]

∠C = ∠C                              [Common]

Then, ΔABC ~ ΔBDC            [By AA similarity]

`therefore"AB"/"BD"="BC"/"DC"`            [Corresponding parts of similar Δ are proportional]

`rArr5.7/3.8="BC"/5.4`

`rArr"BC"=5.7/3.8xx5.4=8.1` cm