In ΔABC, AC = 15 cm and DE || BC. If ADDB=21, then EC = ______.
A
5 cm
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B
12.5 cm
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C
7.5 cm
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D
10 cm
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Solution
The correct option is A 5 cm Given: AC = 15 cm
DE∥ BC ADDB=21
In Δ ADE and Δ ABC, ∠DAE = ∠BAC [ Common ] ∠ADE = ∠ABC and ∠AED = ∠ACB
[ ∵ DE∥ BC, corresponding angles are equal ] ⇒ΔADE ∼ ΔABC [AA similarity]
From Basic Proportionality theorem, ADDB=AEEC ⇒AEEC=21⇒AE=2ECGiven:AC=15cm⇒AE+EC=15cm⇒3EC=15cm⇒EC=5cm