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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"/"DB"=2/3` and AC = 18 cm, find AE
Solution
We have,
`"AD"/"DB"=2/3`and DE || BC
Therefore, by basic proportionality theorem, we have
`"AD"/"DB"="EC"/"AE"`
`rArr3/2="EC"/"AE"`
Adding 1 on both sides, we get
`rArr3/2+1="EC"/"AE"+1`
`rArr(3+2)/2=("EC"+"AE")/"AE"`
`rArr5/2="AC"/"AE"` [∵ AE + EC = AC]
`rArr5/2=18/"AE"` [∵ AC = 18]
`rArr"AE=(18xx2)/5"`
`rArr"AE"=36/5=7.2 " cm"`
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