Question

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

If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find x.

Answer 1

We have,

DE || BC

Therefore, by basic proportionality theorem,

We have,

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

`rArrx/(x-2)=(x+2)/(x-1)`

⇒ x(x − 1) = (x + 2)(x − 2)

⇒ x² − x = x² − (2)²    [∵ (a – b) (a + b) = a² − b2]

⇒ −x = −4

⇒ x = 4 cm

∴ x = 4 cm