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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"=3/4` and AC = 15 cm, find AE
Solution
We have,
`"AD"/"DB"=3/4` and DE || BC
Therefore, by basic proportionality theorem, we have
`"AD"/"DB"="AE"/"EC"`
Adding 1 on both sides, we get
`"AD"/"DB"+1="AE"/"EC"+1`
`3/4+1=("AE"+"EC")/"EC"`
`rArr(3+4)/4="AC"/"EC"` [∵ AE + EC = AC]
`rArr7/4=15/"EC"`
`rArr"EC"=(15xx4)/7`
`rArr"EC"=60/7`
Now, AE + EC = AC
`rArr"AE"+60/7=15`
`rArr"AE"=15-60/7`
`=(105-60)/7`
`=45/7`
= 6.43 cm
∴ AE = 6.42 cm
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