Question

In triangle ABC , 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, then find the value of x.​

Answer 1

In Δ ABC, DE ∥ BC

∴

DB

AD

=

EC

AE

(By basic proportionality theorem)

⇒

x−2

x

=

x−1

x+2

⇒x(x−1)=(x+2)(x−2)

⇒x

2

−x=x

2

−4

⇒x=4.