1. **Problem:** Find the side length of a rhombus given its diagonals are 30 cm and 16 cm. 2. **Formula:** The diagonals of a rhombus bisect each other at right angles. Each side $s$ can be found using the Pythagorean theorem: $$s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Calculation:** - Half of diagonal 1: $\frac{30}{2} = 15$ - Half of diagonal 2: $\frac{16}{2} = 8$ 4. Apply the formula: $$s = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289}$$ 5. Simplify: $$s = 17$$ 6. **Answer:** The side length of the rhombus is **17 cm**.