Given Information:
- Diagonals of the rhombus are of lengths 10 cm and 24 cm.

Find the Side of the Rhombus:
To find the side of the rhombus, we can use the formula that relates the side length, diagonal lengths, and the angle between the diagonals in a rhombus.

Formula:
In a rhombus, the side length (s) can be calculated using the formula:
\[ s = \sqrt{\frac{d_1^2 + d_2^2}{2}} \]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

Calculate the Side Length:
Given that the lengths of the diagonals are 10 cm and 24 cm, we can substitute these values into the formula:
\[ s = \sqrt{\frac{10^2 + 24^2}{2}} \]
\[ s = \sqrt{\frac{100 + 576}{2}} \]
\[ s = \sqrt{\frac{676}{2}} \]
\[ s = \sqrt{338} \]
\[ s \approx 18.39 \text{ cm} \]

Explanation:
The side length of the rhombus is approximately 18.39 cm. This calculation is based on the properties of a rhombus where the diagonals bisect each other at right angles. By applying the formula for the side length of a rhombus in terms of its diagonals, we can find the unknown side length. In this case, the given diagonal lengths are 10 cm and 24 cm, resulting in a side length of approximately 18.39 cm.

Diagonals of a Rhombus
Diagonals of a rhombus are segments that connect opposite vertices of the shape. In a rhombus, the diagonals bisect each other at right angles, and they also bisect the angles of the rhombus.

Given Information
- Length of one diagonal = 10 cm
- Length of the other diagonal = 24 cm

Finding the Side Length
To find the side length of the rhombus, we can use the Pythagorean theorem. The diagonals of a rhombus divide it into four right triangles. Let's label the diagonals as d1 = 10 cm and d2 = 24 cm and the side length as s.
Using the Pythagorean theorem, we have:
\[
s^2 = \left(\dfrac{d1}{2}\right)^2 + \left(\dfrac{d2}{2}\right)^2
\]
\[
s^2 = \left(\dfrac{10}{2}\right)^2 + \left(\dfrac{24}{2}\right)^2
\]
\[
s^2 = 5^2 + 12^2
\]
\[
s^2 = 25 + 144
\]
\[
s^2 = 169
\]
\[
s = \sqrt{169}
\]
\[
s = 13 \text{ cm}
\]
Therefore, the side length of the rhombus is 13 cm.