Question

In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then find the value of x.

Answer 1

In ΔABC, DE||BC

∴ `(AD)/(DB) = (AE)/(EC)`  ...(By basic proportionality theorem)

`\implies x/(x - 2) = (x + 2)/(x - 1)`

`\implies` x(x – 1) = (x + 2) (x – 2)

`\implies` x² – x = x² – 4

`\implies` –x = –4

`\implies` x = 4