Given diagonals are d1 = 12 cm and d2 = 16 cm.

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.

Given diagonals are $d_1 = 12$ cm and $d_2 = 16$ cm.
The half-diagonals are:

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 $c = s$.

The perimeter $P$ of a rhombus is 4 times its side length $s$.

The perimeter of the rhombus is $\text{40 cm}$.