Identify Properties of a Rhombus

The diagonals of a rhombus bisect each other at right angles ($90°$). Therefore, the half-diagonals form a right-angled triangle with the side of the rhombus as the hypotenuse.

$\frac{d_1}{2} = 7\text{ cm}, \quad \frac{d_2}{2} = 24\text{ cm}$

Apply Pythagoras Theorem to Find the Side

Using the relation between the side $a$ and the diagonals $d_1$ and $d_2$, we have $a = \sqrt{(\frac{d_1}{2})^2 + (\frac{d_2}{2})^2}$.

$a = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25\text{ cm}$

Calculate the Perimeter

Since all four sides of a rhombus are equal, the perimeter is given by $4 \times a$.

$\text{Perimeter} = 4 \times 25 = 100\text{ cm}$