Step 1: Understand the properties of a rhombus. A rhombus has four equal sides. Its diagonals bisect each other at right angles. This means that the intersection of the diagonals forms four right-angled triangles, where the legs are half the lengths of the diagonals and the hypotenuse is the side length of the rhombus. Step 2: Determine the lengths of the half-diagonals. Given diagonals are $d_1 = 12$ cm and $d_2 = 16$ cm. The half-diagonals are: $$ \frac{d_1}{2} = \frac{12}{2} = 6 \text{ cm} $$ $$ \frac{d_2}{2} = \frac{16}{2} = 8 \text{ cm} $$ Step 3: Use the Pythagorean theorem to find the side length of the rhombus. Let $s$ be the side length of the rhombus. In a right-angled triangle formed by the half-diagonals and a side, the Pythagorean theorem states $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. Here, $a = 6$ cm, $b = 8$ cm, and $c = s$. $$ s^2 = (6 \text{ cm})^2 + (8 \text{ cm})^2 $$ $$ s^2 = 36 \text{ cm}^2 + 64 \text{ cm}^2 $$ $$ s^2 = 100 \text{ cm}^2 $$ $$ s = \sqrt{100 \text{ cm}^2} $$ $$ s = 10 \text{ cm} $$ Step 4: Calculate the perimeter of the rhombus. The perimeter $P$ of a rhombus is $4$ times its side length $s$. $$ P = 4s $$ $$ P = 4 \times 10 \text{ cm} $$ $$ P = 40 \text{ cm} $$ The perimeter of the rhombus is $\boxed{\text{40 cm}}$.