The lengths of the diagonals of a rhombus are 5 cm and 12 cm. The length of each side of the rhombus is:

1. 13 cm

2. 6.5 cm

3. 6.25 cm

4. 5.25 cm

Let AC = 5 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 = 2.5 cm.

In right triangle AOB,

By pythagoras theorem we get,

Hypotenuse² = Base² + Height²

⇒ AB² = AO² + OB²

⇒ AB² = (2.5)² + 6²

⇒ AB² = 6.25 + 36

⇒ AB² = 42.25

⇒ AB = $\sqrt{42.25}$ = 6.5 cm.

∴ The length of each side of the rhombus is 6.5 cm.

Hence, option 2 is the correct option.