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Question

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 ]
ΔADEΔABC [AA similarity]
From Basic Proportionality theorem,
ADDB=AEEC
AEEC=21AE=2ECGiven: AC=15cmAE+EC=15cm3EC=15cmEC=5cm

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