Identify Diagonals

The diagonals of the rhombus are given as $d_1 = 6\text{ cm}$ and $d_2 = 8\text{ cm}$. Diagonals of a rhombus bisect each other at right angles ($90°$).

$d_1 = 6\text{ cm}, \quad d_2 = 8\text{ cm}$

Find the Half-Diagonals

The halves of the diagonals form the legs of a right-angled triangle whose hypotenuse is the side $a$ of the rhombus.

$\frac{d_1}{2} = 3\text{ cm}, \quad \frac{d_2}{2} = 4\text{ cm}$

Calculate Side Length using Pythagorean Theorem

Applying Pythagoras theorem on the right triangle formed by half-diagonals: $a = \sqrt{(\frac{d_1}{2})^2 + (\frac{d_2}{2})^2}$.

$a = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\text{ cm}$

Calculate the Perimeter

Since all four sides of a rhombus are equal, the perimeter is $4$ times the side length $a$.

$\text{Perimeter} = 4 \times a = 4 \times 5 = 20\text{ cm}$