Identify Half-Diagonals

The diagonals of a rhombus bisect each other perpendicularly at $90°$. Thus, the lengths of the half-diagonals are $d_1/2 = 7\text{ cm}$ and $d_2/2 = 24\text{ cm}$.

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

Apply Pythagorean Theorem

Each side $a$ of the rhombus forms the hypotenuse of a right-angled triangle whose legs are the half-diagonals.

$a = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}$

Calculate the Side Length

Substitute the values of the half-diagonals into the formula to find the side length $a$.

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

Calculate the Perimeter

Since all four sides of a rhombus are equal, multiply the side length by $4$ to get the perimeter.

$P = 4 \times a = 4 \times 25 = 100\text{ cm}$