The problem involves calculating the length of $YZ$ in a right triangle using Pythagoras' theorem. Here’s the solution step-by-step:

Given:

• The length of $XY = 9 \, \text{cm}$
• The length of $XZ = 16 \, \text{cm}$
• $YZ$ is the hypotenuse.

Pythagoras' theorem states: $YZ^2 = XY^2 + XZ^2$

Step 1: Square the given sides

$XY^2 = 9^2 = 81$ $XZ^2 = 16^2 = 256$

Step 2: Add the squares

$YZ^2 = 81 + 256 = 337$

Step 3: Take the square root

$YZ = \sqrt{337} \approx 18.4 \, \text{cm}$

Final Answer:

The length of $YZ$ is approximately 18.4 cm to 1 decimal place.

Would you like further clarification or more details on any step? Here are some related questions you might explore:

1. How can Pythagoras' theorem be applied to real-life problems?
2. What happens when one of the sides is missing and not the hypotenuse?
3. How does Pythagoras’ theorem relate to the distance formula in coordinate geometry?
4. Can Pythagoras' theorem be used in 3D problems?
5. What are some proofs of Pythagoras’ theorem?

Tip: Always double-check the units of measurement to avoid confusion!