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Question

In triangle ABC, DE is parallel to BC; where D and E are the points on AB and AC respectively. Also, if AD = 12 cm, BD = 24 cm and BC = 8 cm, the length of DE is


A

23 cm

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B

34 cm

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C

223 cm

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D

234 cm

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Solution

The correct option is C

223 cm


In ΔABC, DEBC

ADE=ABC (Corresponding angles)

and AED=ACB

Now, in ΔADE and ΔABC

ADE=ABC (Proved)

AED=ACB (Proved)

A=A (Common)

ΔADEΔABC (AA Postulate)

ADAB=AEAC=DEBC

ADAD+DB=DEBC212+24=DE8

( AD = 12 cm, DB = 24 cm and BC = 8 cm)

1236=DE8

DE=12×836=83=223 cm


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