The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of the side of rhombus is

1. 9 cm

2. 10 cm

3. 8 cm

4. 20 cm

Let AC = 16 cm and BD = 12 cm.

We know that,

Diagonals of rhombus are perpendicular and bisect each other,

OB = $\dfrac{1}{2}BD$ = 6 cm and AO = $\dfrac{1}{2}$AC = 8 cm.

In right triangle AOB,

By pythagoras theorem we get,

⇒ AB² = AO² + OB²

⇒ AB² = 8² + 6²

⇒ AB² = 64 + 36

⇒ AB² = 100

⇒ AB = $\sqrt{100}$ = 10 cm.

Hence, Option 2 is the correct option.