Question

In the following figure, point D divides AB in the ratio 3 : 5. Find :

DE = 2.4 cm, find the length of BC.

Answer 1

Given that `(AD)/(DB) = 3/5`

So, `(AD)/(AB) = 3/8`

In ΔADE and ΔABC,

∠ADE = ∠ABC  ...(Since DE || BC, so the angles are corresponding angles)

∠A = ∠A    ...(Common angle)

∴ ΔADE ∼ ΔABC  ...(AA criterion for similarity)

`=> (AD)/(AB) = (DE)/(BC)`

`=> 3/8 = (2.4)/(BC)`

`=>` BC = 6.4 cm