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.