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

Answer 1

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