Question

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

If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.

Answer 1

We have,

DE || BC

Therefore, by basic proportionally theorem,

We have

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

`rArr6/9=8/"EC"`

`rArr2/3=8/"EC"`

`rArr"EC"=(8xx3)/2`

⇒ EC = 12 cm

⇒ Now, AC = AE + EC = 8 + 12 = 20 cm

∴ AC = 20 cm

Answer 2

Apply Basic Proportionality Theorem

`(AD)/(AB) = (AE)/(AC)`

`6/15 = 8/(AC)`

`6/15 = 8/(AC) => 6xxAC = 15xx8 => 6xxAC = 120 => AC = 120/6 = 20 cm`

AC = 20 cm