The perimeter of a rhombus can be found by adding the lengths of all its sides. In order to find the perimeter, we need to determine the length of each side of the rhombus.

Given that the diagonals of the rhombus measure 16cm and 30cm, we can use the properties of a rhombus to find the length of each side.

The diagonals of a rhombus bisect each other at right angles. This means that they divide the rhombus into four congruent right-angled triangles.

Using the Pythagorean theorem, we can find the length of each side of the rhombus by applying it to one of these triangles.

Let's consider one of the congruent triangles formed by the diagonals.

Using Pythagorean theorem:

- The length of one side of the rhombus is the hypotenuse of the right-angled triangle.
- The length of the other two sides are the legs of the right-angled triangle, which are half the lengths of the diagonals.

Using the given information, we have:
- Hypotenuse = 16cm
- Legs = 30cm / 2 = 15cm

Applying the Pythagorean theorem:
Hypotenuse^2 = Leg^2 + Leg^2

16^2 = 15^2 + 15^2
256 = 225 + 225
256 = 450

Thus, we have obtained a contradiction. The lengths of the given diagonals do not form a right-angled triangle. Therefore, it is not possible to find the length of each side of the rhombus and hence its perimeter.

In conclusion, it is not possible to determine the perimeter of the rhombus with the given information.