1. **Problem statement:** We have a right triangle XYZ with a right angle at vertex Y. The side XY is 9 cm, the hypotenuse XZ is 17 cm, and we need to find the length of side YZ. 2. **Formula used:** According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: $$XZ^2 = XY^2 + YZ^2$$ 3. **Rearranging the formula to find YZ:** $$YZ^2 = XZ^2 - XY^2$$ 4. **Substitute the known values:** $$YZ^2 = 17^2 - 9^2 = 289 - 81 = 208$$ 5. **Calculate YZ:** $$YZ = \sqrt{208}$$ 6. **Simplify the square root:** $$\sqrt{208} = \sqrt{16 \times 13} = 4\sqrt{13}$$ 7. **Approximate the decimal value:** $$YZ \approx 4 \times 3.6055 = 14.422$$ 8. **Round to 1 decimal place:** $$YZ \approx 14.4\text{ cm}$$ **Final answer:** The length of side YZ is approximately 14.4 cm.