Question

In the given figure, DE || BC.
(1) Prove that : AADE - AABC.
(ii) Given that AD = 1/2DB, calculate DE, if BC = 4.5 cm.

Answer 1

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DE ║ BC

=> ΔADE ≈ ΔABC

AD/AB = DE/BC  = AE/AC

AD/AB  = AD /(AD + BD)

AD = BD/2

=> BD = 2AD

= AD/(AD + 2AD)

= AD/3AD

= 1/3

=> DE/BC = 1/3

=> DE = BC/3

BC = 4.5

=> DE = 4.5/3

=> DE = 1.5 cm

DE = 1.5 cm

Learn more:

In the given figure, AD = 1.28 cm, DB = 2.56cm AE = 0.64 cm. DE will