Question

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

Options

• 3 : 8

• 3 : 5

• 5 : 3

• 8 : 3

Answer 1

In the given figure, DE is parallel to BC. If AD : BD = 3 : 5 then DE : BC is 3 : 8.

Explantion:

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.

∴ `(DE)/(BC) = (AD)/(AB)`

⇒ `(DE)/(BC) = (3x)/(8x)`

⇒ `(DE)/(BC) = 3/8`

⇒ DE : BC = 3 : 8