**Finding the length of the sides of a rhombus**

A rhombus is a quadrilateral with four equal sides. In order to find the length of its sides, we need to use the given information about the lengths of its diagonals.

**Given information:**

- Length of one diagonal: 24 cm
- Length of the other diagonal: 10 cm

**Using the properties of a rhombus:**

A rhombus has several properties that can help us find the length of its sides. Two important properties are:

1. The diagonals of a rhombus bisect each other at right angles.
2. The diagonals of a rhombus are perpendicular bisectors of each other.

**Using the first property:**

Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the length of one side of the rhombus.

Let's consider one-half of the diagonal lengths:

- Half of the first diagonal: 24 cm / 2 = 12 cm
- Half of the second diagonal: 10 cm / 2 = 5 cm

Using the Pythagorean theorem, we can find the length of one side of the rhombus:

Side^2 = (12 cm)^2 - (5 cm)^2
Side^2 = 144 cm^2 - 25 cm^2
Side^2 = 119 cm^2

Taking the square root of both sides, we get:

Side = √119 cm

So, the length of one side of the rhombus is approximately 10.92 cm.

**Using the second property:**

Since the diagonals of a rhombus are perpendicular bisectors of each other, we can create right-angled triangles using half of the diagonal lengths.

Let's consider the right-angled triangle formed by half of the first diagonal, half of the second diagonal, and one side of the rhombus.

Using the Pythagorean theorem, we can find the length of the side of the rhombus:

Side^2 = (12 cm)^2 - (5 cm)^2
Side^2 = 144 cm^2 - 25 cm^2
Side^2 = 119 cm^2

Taking the square root of both sides, we get:

Side = √119 cm

So, the length of one side of the rhombus is approximately 10.92 cm.

**Conclusion:**

The length of one side of the rhombus is approximately 10.92 cm. Since a rhombus has four equal sides, all four sides of the rhombus will also have a length of approximately 10.92 cm.