Question

In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC

If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.

Answer 1

We have,

AD = 2 cm, AB = 6 cm

∴ DB = AB – AD

= 6 – 2

⇒ DB = 4 cm

And, DE || BC

Therefore, by basic proportionality theorem, we have,

`"AD"/"DB"="AE"/"EC"`

Taking reciprocal on both sides, we get,

`"DB"/"AD"="EC"/"AE"`

`4/2="EC"/"AE"`

Adding 1 on both sides, we get

`4/2+1="EC"/"AE"+1`

`rArr(4+2)/2=("EC"+"AE")/"AE"`

`rArr6/2="AC"/"AE"`         [∵ EC + AE = AC]

`rArr6/2=9/"AE"`              [∵ AC = 9cm]

`"AE"=(9xx2)/6`

⇒ AE = 3 cm