Given:
- The length of the two diagonals of a rhombus is 16 cm and 12 cm.

To find:
- The perimeter of the rhombus.

Approach:
- A rhombus is a quadrilateral with all four sides equal in length.
- The diagonals of a rhombus are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other into two equal parts.
- Let's label the diagonals as AC and BD, with AC = 16 cm and BD = 12 cm.
- The intersection point of the diagonals is O, which is also the center of the rhombus.
- The diagonals divide the rhombus into four congruent right-angled triangles, AOB, BOC, COD, and DOA.
- The lengths of the diagonals and the right angles at the intersection point O allow us to use the Pythagorean theorem to find the lengths of the sides of the rhombus.
- Once we have the lengths of the sides, we can calculate the perimeter by adding all four sides together.

Solution:
1. Using the Pythagorean theorem, we can find the lengths of the sides of the rhombus.
- In triangle AOB, AB is the hypotenuse, and AO and OB are the legs.
- Using the Pythagorean theorem, we have: AB² = AO² + OB²

2. Finding the lengths of AO and OB:
- Since the diagonals of a rhombus bisect each other, AO = OB = 1/2 * AC = 1/2 * 16 cm = 8 cm.

3. Substituting the values into the Pythagorean theorem:
- AB² = 8² + 8²
- AB² = 64 + 64
- AB² = 128
- AB = √128
- AB = 8√2 cm

4. The length of each side of the rhombus is AB = 8√2 cm.

5. The perimeter of the rhombus is the sum of all four sides:
- Perimeter = 4 * AB
- Perimeter = 4 * 8√2 cm
- Perimeter = 32√2 cm

Answer:
- The perimeter of the rhombus is 32√2 cm.