Explanation:

Given:
- Diagonals of the rhombus measure 16 cm and 30 cm

Using Pythagorean Theorem:
- In a rhombus, the diagonals bisect each other at right angles, forming four right triangles.
- The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- Let the sides of the rhombus be a and b, where a is half of the diagonal measuring 30 cm and b is half of the diagonal measuring 16 cm.
- Using Pythagorean theorem, we can form the following equations:
- a² + b² = (side length)²
- (30/2)² + (16/2)² = (side length)²
- 15² + 8² = (side length)²
- 225 + 64 = (side length)²
- 289 = (side length)²
- side length = √289
- side length = 17 cm

Calculating Perimeter:
- The perimeter of a rhombus is the sum of all its four sides.
- Since all sides of a rhombus are equal, the perimeter is 4 times the length of one side.
- Therefore, the perimeter of the rhombus is 4 * 17 cm = 68 cm

Conclusion:
- The perimeter of the rhombus is 68 cm.