1. **Problem statement:** We have a right triangle XYZ with a right angle at Y. The sides XY and XZ are given as 9 cm and 16 cm respectively, 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 (the side opposite the right angle) equals the sum of the squares of the other two sides. 3. **Identify the hypotenuse:** Since the right angle is at Y, the hypotenuse is side XZ, which is 16 cm. 4. **Apply Pythagoras' theorem:** $$XZ^2 = XY^2 + YZ^2$$ Substitute the known values: $$16^2 = 9^2 + YZ^2$$ 5. **Calculate squares:** $$256 = 81 + YZ^2$$ 6. **Isolate $YZ^2$:** $$YZ^2 = 256 - 81$$ $$YZ^2 = 175$$ 7. **Find $YZ$ by taking the square root:** $$YZ = \sqrt{175}$$ 8. **Simplify the square root:** $$YZ = \sqrt{25 \times 7} = 5\sqrt{7}$$ 9. **Calculate the decimal value:** $$YZ \approx 5 \times 2.6458 = 13.229$$ 10. **Round to 1 decimal place:** $$YZ \approx 13.2$$ cm **Final answer:** The length of side YZ is approximately 13.2 cm.