Question

In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC. If `(AD)/(DB) = 2/3` and AC = 18 cm, find AE.

Answer 1

We have,

`(AD)/(DB) = 2/3` and DE || BC

Therefore, by basic proportionality theorem, we have

AD = 2, DB = 3

A-D-B = AD + DB

AB = 2 + 3

AB = 5

`(AD)/(AB) = (AE)/(AC)`

`rArr2/5 = (AE)/(AC)`

`rArr2/5 = (AE)/(18)`   ... [∵ AC = 18]

`rArrAE = (18 xx 2)/5`

`rArrAE = 36/5`

= 7.2 cm