https://file.aiquickdraw.com/mathbot/file/1724503369311qqaqyon7.jpg

To solve this problem using Pythagoras' theorem, we can observe that we have a right-angled triangle \(XYZ\), where:

- Side \(XY\) is the base of the triangle with a length of 9 cm.
- Side \(XZ\) is the height of the triangle with a length of 16 cm.
- Side \(YZ\) is the hypotenuse, which we need to find.

### Step-by-Step Solution:

1. **Identify the sides**: In a right-angled triangle, the hypotenuse is the side opposite the right angle. Here, \(YZ\) is the hypotenuse.

2. **Apply Pythagoras' theorem**:
   \[
   \text{Pythagoras' theorem: } a^2 + b^2 = c^2
   \]
   Here, \(a\) and \(b\) are the lengths of the legs (base and height), and \(c\) is the length of the hypotenuse. Substituting the values, we get:
   \[
   XY^2 + XZ^2 = YZ^2
   \]

   \[
   9^2 + 16^2 = YZ^2
   \]

3. **Calculate the squares**:
   \[
   9^2 = 81
   \]
   \[
   16^2 = 256
   \]

4. **Add the squares**:
   \[
   81 + 256 = 337
   \]

5. **Find the square root to get \(YZ\)**:
   \[
   YZ = \sqrt{337}
   \]
   \[
   YZ \approx 18.357
   \]

   Rounding this to 1 decimal place:
   \[
   YZ \approx 18.4 \text{ cm}
   \]

### Conclusion:
The length of \(YZ\) is approximately 18.4 cm when rounded to 1 decimal place.

Would you like more details or have any questions?

Here are some related questions that you might find interesting:

1. What is the Pythagorean theorem, and how is it applied in different types of triangles?
2. How do you calculate the area of a right-angled triangle using the base and height?
3. What are the properties of right-angled triangles that make Pythagoras' theorem applicable?
4. How can the Pythagorean theorem be used in real-world applications?
5. How can you determine whether a triangle is right-angled if you know the lengths of all three sides?

**Tip**: When dealing with right-angled triangles, always ensure you correctly identify the hypotenuse, as it is always the longest side opposite the right angle.

Explore how to solve a right-angled triangle problem using Pythagoras' theorem with a step-by-step solution. This problem involves calculating the length of the hypotenuse in a triangle with sides 9 cm and 16 cm. Suitable for Grades 7-9 mathematics students.

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