Question

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

If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.

Answer 1

We have, DE || BC

Therefore, by basic proportionality theorem, we have,

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

`rArr2.5/3.0=3.75/"EC"`

`rArr"EC"=(3.75xx3)/2.5=(375xx3)/250`

`rArr"EC"=(15xx3)/10=45/10=4.5` cm

Now, AC = AE + EC = 3.75 + 4.5 = 8.25

∴ AC = 8.25 cm