**Answer:**

Given information:
- The diagonals of the rhombus are of lengths 10 cm and 24 cm.

To find the length of each side of the rhombus, we can use the property of a rhombus where the diagonals bisect each other at right angles and divide the rhombus into four congruent right-angled triangles.

**Step 1: Find the length of each diagonal**

The diagonals of the rhombus are of lengths 10 cm and 24 cm.

**Step 2: Find the measure of the right-angled triangle**

Since the diagonals bisect each other at right angles, each of the four right-angled triangles formed is a 30-60-90 triangle. In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Let's consider one of the right-angled triangles formed by the diagonals:

- The hypotenuse of the triangle is half of the diagonal length, which is half of 10 cm = 5 cm.
- One of the legs of the triangle is half of the other diagonal length, which is half of 24 cm = 12 cm.
- The remaining leg of the triangle can be found using the Pythagorean theorem:
- (leg)^2 + (12 cm)^2 = (5 cm)^2
- (leg)^2 + 144 cm^2 = 25 cm^2
- (leg)^2 = 25 cm^2 - 144 cm^2
- (leg)^2 = 625 cm^2 - 144 cm^2
- (leg)^2 = 481 cm^2
- leg = √481 cm ≈ 21.93 cm

**Step 3: Find the length of each side of the rhombus**

Since the rhombus is made up of four congruent right-angled triangles, the length of each side is equal to the length of the leg of the triangle.

Therefore, the length of each side of the rhombus is approximately 21.93 cm.

The closest option to this answer is option 'B' with a length of 13 cm.

Let the side of rhombus is x.
Diagonals of a rhombus are bisect each other a right angle.
so half of diagonals 5cm and 12cm are makes a right angled triangle.
Then by pythogoras theorum
=> x²=5²+12²
=> x² =25+144
=> x=√169
=> x= 13
hence, the side of rhombus is 13cm.