https://file.aiquickdraw.com/mathbot/file/1736926342954fd2kj6o3.jpg

We can solve this problem using **Pythagoras' Theorem**, which states:

\[
c^2 = a^2 + b^2
\]

Where \(c\) is the hypotenuse (the longest side), and \(a\) and \(b\) are the other two sides of the right triangle.

### Given:
- Hypotenuse (\(PQ\)) = \(9 \, \text{cm}\)
- One side (\(PR\)) = \(4 \, \text{cm}\)
- Unknown side (\(QR\)) = ?

Rearranging the formula for \(QR\):

\[
QR^2 = PQ^2 - PR^2
\]

Substituting the values:

\[
QR^2 = 9^2 - 4^2
\]

\[
QR^2 = 81 - 16
\]

\[
QR^2 = 65
\]

Taking the square root:

\[
QR = \sqrt{65} \approx 8.1 \, \text{cm}
\]

### Final Answer:
The length of \(QR\) is approximately **8.1 cm** (to 1 decimal place).

---

Would you like further details or clarifications? 😊  

### 5 Related Questions:
1. How does Pythagoras' theorem work for triangles with different units?
2. Can Pythagoras' theorem be used in three dimensions?
3. What are some real-world applications of this theorem?
4. How do you verify if a triangle is a right triangle using side lengths?
5. How would the calculation change if one of the sides was unknown instead of the hypotenuse?

### Tip:
Always check that the triangle is a right triangle before applying Pythagoras' theorem!

Using Pythagoras' theorem, calculate the length of QR. Give your answer to 1 d.p.

Learn how to calculate the length of QR in a right triangle using Pythagoras' theorem. The hypotenuse is 9 cm, and one side is 4 cm. Step-by-step solution provided. Suitable for Grades 7-10 students.

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