Question

The diagonal BD of the parallelogram ABCD is divided by the segment AE in a ratio of 1 : 2. If BE = 1.8 cm, find the length of AD.

Answer 1

Given: In parallelogram ABCD,

The diagonal BD is divided by segment AE in the ratio 1 : 2.

So, `(BO)/(OD) = 1/2`

BE = 1.8 cm

To find: The length of AD.

In ΔBOE and ΔAOD

∠BOE = ∠AOD   ...(Vertically opposite angles)

∠OBE = ∠ODA   ...(Alternate interior angles)

∴ ΔBOE ∼ ΔAOD   ...(AA similarity)

∴ `(BE)/(AD) = (BO)/(OD)`

⇒ `1.8/(AD) = 1/2`

⇒ AD = 1.8 × 2   ...(By cross multiplying)

⇒ AD = 3.6 cm

Therefore, the length of AD is 3.6 cm.