1. **State the problem:** We need to find the length of side $YZ$ in a right triangle $XYZ$ where $XY = 5$ cm and $XZ = 19$ cm. The right angle is at $Y$, so $YZ$ is perpendicular to $XY$. 2. **Formula used:** By 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. **Substitute known values:** $$19^2 = 5^2 + YZ^2$$ 4. **Calculate squares:** $$361 = 25 + YZ^2$$ 5. **Isolate $YZ^2$:** $$YZ^2 = 361 - 25$$ $$YZ^2 = 336$$ 6. **Find $YZ$ by taking the square root:** $$YZ = \sqrt{336}$$ 7. **Simplify the square root:** $$YZ = \sqrt{16 \times 21} = 4\sqrt{21}$$ 8. **Calculate decimal value:** $$YZ \approx 4 \times 4.5826 = 18.3304$$ 9. **Round to 1 decimal place:** $$YZ \approx 18.3$$ cm **Final answer:** The length of $YZ$ is approximately **18.3 cm**.