In the given figure, AB || CD, AB = 12 cm, OB = (3x + 3) cm, CD = 5x cm and OC = (6x + 1) cm. Find the value of x.

In △OAB and △OCD,

∠AOB = ∠COD (Vertically opposite angles are equal)

∠OAB = ∠ODC (Alternate angles are equal)

△OAB ~ △OCD [By A.A. axiom]

We know that,

Ratio of corresponding sides of similar triangle are proportional.

$\therefore \dfrac{AB}{CD} = \dfrac{OB}{OC} \\[1em] \Rightarrow \dfrac{12}{5x} = \dfrac{3x + 3}{6x + 1} \\[1em] \Rightarrow 12(6x + 1) = 5x(3x + 3) \\[1em] \Rightarrow 72x + 12 = 15x^2 + 15x \\[1em] \Rightarrow 15x^2 + 15x - 72x - 12 = 0 \\[1em] \Rightarrow 15x^2 - 57x - 12 = 0 \\[1em] \Rightarrow 15x^2 - 60x + 3x - 12 = 0 \\[1em] \Rightarrow 15x(x - 4) + 3(x - 4) = 0 \\[1em] \Rightarrow (15x + 3)(x - 4) = 0 \\[1em] \Rightarrow 15x + 3 = 0 \text{ or } x - 4 = 0 \\[1em] \Rightarrow x = -\dfrac{3}{15} \text{ or } x = 4.$

Since, length cannot be negative.

Hence, x = 4.