Question

If in a triangle ABC, D and E are on the sides AB and AC such that, DE is parallel to BC and `(AD)/(BD) = 3/5`. If AC = 4 cm, then AE is

Options

• 1.5 cm

• 2.0 cm

• 1.8 cm

• 2.4 cm

Answer 1

1.5 cm

Explanation:

DE || BC 

∴ `(AD)/(AB) = (AE)/(AC)`

`(AD)/(BD) = 3/5`

⇒ `(BD)/(AD) = 5/3`

⇒ `(BD)/(AD) + 1 = 5/3 + 1`

⇒ `(BD + AD)/(AD) = (5 + 3)/3`

∴ `(AD)/(AB) = (AE)/(AC)`

⇒ `3/8 = (AE)/4`

⇒ AE = `(3 xx 4)/8`

= 1.5 cm