Identify Given Properties of Rhombus

Let the lengths of the diagonals of the rhombus be $d_1 = 7\text{ cm}$ and $d_2 = 24\text{ cm}$. In a rhombus, diagonals bisect each other at right angles ($90°$).

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

Calculate the Length of Side of Rhombus

Using the relationship between the side $a$ and diagonals $d_1, d_2$ derived from Pythagoras theorem: $a = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2} = \frac{1}{2}\sqrt{d_1°2 + d_2°2}$.

$a = \frac{1}{2}\sqrt{7°2 + 24°2} = \frac{1}{2}\sqrt{49 + 576} = \frac{1}{2}\sqrt{625} = \frac{25}{2} = 12.5\text{ cm}$

Calculate the Perimeter

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

$P = 4 \times 12.5 = 50\text{ cm}$