Assertion (A): The area of rhombus is 84 cm². If its one diagonal is 7 cm, then side of the rhombus is 12 cm.

Reason (R): Area of rhombus is given by $\dfrac{1}{2}$ × product of its diagonals.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

By formula,

$\Rightarrow \text{Area of rhombus} = \dfrac{1}{2} \times d$1 \times d2 \\[1em] \Rightarrow 84 = \dfrac{1}{2} × 7 × d2 \\[1em] \Rightarrow d2 = \dfrac{168}{7} \\[1em] \Rightarrow d_2 = 24 \text{ cm}.

Now in rhombus diagonals bisect each other at right angles.

Thus,

By pythagras theorem,

(Side)² = $\Big(\dfrac{d$1}{2}\Big)^2 + \Big(\dfrac{d2}{2}\Big)^2

(Side)² = $\Big(\dfrac{7}{2}\Big)^2 + \Big(\dfrac{24}{2}\Big)^2$

(Side)² = (3.5)² + (12)²

(Side)² = 12.25 + 144

(Side)² = 156.25

Side = $\sqrt{156.25}$

Side = 12.5 cm

∴ Assertion (A) is false.

By formula,

Area of rhombus = $\dfrac{1}{2}$ × product of its diagonals

∴ Reason (R) is true.

Assertion (A) is false, reason (R) is true.

Hence, option 2 is the correct option.