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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.
Solution
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
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