Question

In the given diagram OC = 1.5 × OA, then OB is equal to ______.

Options

• 3 × OD

• 1.5 × OD

• `2/3 xx` OD

• OD

Answer 1

In the given diagram OC = 1.5 × OA, then OB is equal to `bbunderline(2/3 xx OD)`.

Explanation:

From figure,

In △ OAB and △ OCD,

⇒ ∠AOB = ∠COD (Vertically opposite angles are equal)

⇒ ∠OAB = ∠OCD (Alternate angles are equal)

⇒ ∠OBA = ∠ODC (Alternate angles are equal)

∴ △ OAB ~ △ OCD (By A.A.A. postulate)

Given,

⇒ OC = 1.5 × OA

⇒ `(OA)/(OC) = 1/1.5 = 2/3`

We know that,

Corresponding sides of similar triangle are in proportion.

∴ `(OB)/(OD) = (OA)/(OC)` 

⇒ `(OB)/(OD) = 2/3`

⇒ OB = `2/3` × OD