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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, DE∥BC ∴∠ADE=∠ABC (Corresponding angles) and ∠AED=∠ACB Now, in ΔADE and ΔABC ∠ADE=∠ABC (Proved) ∠AED=∠ACB (Proved) ∠A=∠A (Common) ∴ΔADE∼ΔABC (AA Postulate) ∴ADAB=AEAC=DEBC ⇒ADAD+DB=DEBC⇒212+24=DE8 (∴ AD = 12 cm, DB = 24 cm and BC = 8 cm) ⇒1236=DE8 ∴DE=12×836=83=223 cm

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