Question

In the following figure, point D divides AB in the ratio 3 : 5. Find : `(AE)/(AC)`

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) = (AE)/(AC)`

`=> (AE)/(AC) = 3/8`