- **Given information**:
- Diagonals of the rhombus measure 16 cm and 30 cm.
- **Formula**:
- In a rhombus, the diagonals bisect each other at right angles. The length of each side of the rhombus can be calculated using the Pythagorean theorem.
- **Calculations**:
- Let the diagonals of the rhombus be \(d_1 = 16\) cm and \(d_2 = 30\) cm.
- The formula for finding the side of a rhombus is \(a = \sqrt{\frac{d_1^2 + d_2^2}{2}}\).
- Substituting the given values, we get \(a = \sqrt{\frac{16^2 + 30^2}{2}} = \sqrt{\frac{256 + 900}{2}} = \sqrt{\frac{1156}{2}} = \sqrt{578} \approx 24.04\) cm.
- **Perimeter of the rhombus**:
- The perimeter of a rhombus is given by \(4a\), where \(a\) is the side length.
- Substituting the calculated value of \(a\), we get the perimeter \(= 4 \times 24.04 \approx 96.16\) cm.
- **Conclusion**:
- The perimeter of the rhombus with diagonals measuring 16 cm and 30 cm is approximately 96.16 cm.