In the given figure, DE is parallel to BC. If AD : BD = 3 : 5 then DE : BC is :

1. 3 : 8

2. 3 : 5

3. 5 : 3

4. 8 : 3

From figure,

In △ DAE and △ BAC,

⇒ ∠DAE = ∠BAC (Common angle)

⇒ ∠EDA = ∠CBA (Corresponding angles are equal)

∴ △ DAE ~ △ BAC (By A.A. postulate)

Given,

AD : BD = 3 : 5

Let AD = 3x and BD = 5x.

From figure,

AB = AD + BD = 3x + 5x = 8x.

We know that,

Corresponding sides of similar triangle are in proportion.

$\therefore \dfrac{DE}{BC} = \dfrac{AD}{AB} \\[1em] \Rightarrow \dfrac{DE}{BC} = \dfrac{3x}{8x} \\[1em] \Rightarrow \dfrac{DE}{BC} = \dfrac{3}{8} \\[1em] \Rightarrow DE : BC = 3 : 8.$

Hence, Option 1 is the correct option.