In the given figure, AB ∥ CD and OA = (2x + 4) cm, OB = (9x − 21) cm, OC = (2x − 1) cm and OD = 3 cm. Then x equals:

1. 2.1

2. 3

3. 4

4. 6

Given,

OA = (2x + 4) cm

OB = (9x − 21) cm

OC = (2x − 1) cm

OD = 3 cm

In ΔOAB and ΔOCD

∠COD = ∠AOB [Vertically Opposite Angles are equal]

∠OAB = ∠OCD [alternate interior angles are equal]

∴ ΔOAB ∼ ΔOCD by AA similarity. Then ratios of corresponding sides are equal :

$\Rightarrow \dfrac{OA}{OC} = \dfrac{OB}{OD} \\[1em] \Rightarrow \dfrac{(2x + 4)}{(2x - 1)} = \dfrac{(9x - 21)}{3} \\[1em] \Rightarrow 3 \times (2x + 4) = (2x - 1) \times (9x - 21) \\[1em] \Rightarrow 6x + 12 = 18x^2 - 42x -9x +21 \\[1em] \Rightarrow 18x^2 - 42x -9x +21 - 6x - 12 = 0\\[1em] \Rightarrow 18x^2 - 42x - 9x - 6x +21 - 12 = 0\\[1em] \Rightarrow 18x^2 - 57x + 9 = 0\\[1em] \Rightarrow 18x^2 - 54x - 3x + 9 = 0\\[1em] \Rightarrow 18x(x - 3) - 3(x - 3) = 0\\[1em] \Rightarrow (18x - 3)(x - 3) = 0\\[1em] \Rightarrow (18x - 3) = 0 \text{ or }(x - 3) = 0 \\[1em] \Rightarrow 18x = 3 \text{ or } x = 3 \\[1em] \Rightarrow x = \dfrac{3}{18} \text{ or } x = 3 \\[1em] \Rightarrow x = \dfrac{1}{6} \text{ or } x = 3.$

x cannot be $\dfrac{1}{6}$ as it yields negative OB and OC values. Therefore x = 3.

Hence, option 2 is the correct option.