In a ∆ ABC, DE || BC. D and E lie on AB and AC respectively.

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In a ∆ ABC, DE || BC. D and E lie on AB and AC respectively.

Home » Aptitude » Plane Geometry » Question

In a ∆ ABC, DE || BC. D and E lie on AB and AC respectively. If AB = 7 cm and BD = 3 cm, then find BC : DE.

1. 2 : 3
2. 3 : 2
3. 3.5 : 2
4. 7 : 2

Correct Option: C

We draw a figure triangle ABC in which DE || BC. D and E lie on AB and AC respectively,

DE || BC
∴ ∠ADE = ∠ABC
∠AED = ∠ACB
∴ By AA - similarity theorem,
∆ ADE ~ ∆ ABC
AB = BC
AD DE

⇒ AB = BC
AB - BD DE

⇒ 7 = BC
7 - 3 DE

⇒ BC = 7 = 3.5 = 3.5 : 2
DE 4 2