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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.
Solution
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
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