In the given figure DE || BC, the value of x is:

The correct answer is Option (2) → 11

By the basic proportionality theorem (Thales’ theorem), a line drawn parallel to one side of a triangle divides the other two sides in the same ratio. Since DE ∥ BC, \(\displaystyle\frac{AD}{DB}=\frac{AE}{EC}\).

• With AD = \(x-2\), DB = 3, AE = 15 and EC = 5: \(\displaystyle\frac{x-2}{3}=\frac{15}{5}=3\)

• \(x-2=9\), so \(x=11\)