To solve for the length of side $QR$ using Pythagoras' theorem, we can use the formula:

$c^2 = a^2 + b^2$

Where:

• $c$ is the hypotenuse (side $QR$ in this case),
• $a$ and $b$ are the two other sides.

From the diagram:

• $PQ = 9 \, \text{cm}$,
• $PR = 4 \, \text{cm}$,
• We need to calculate $QR$.

Using the Pythagorean theorem: $QR^2 = PQ^2 + PR^2$ Substituting the values: $QR^2 = 9^2 + 4^2 = 81 + 16 = 97$ $QR = \sqrt{97} \approx 9.8 \, \text{cm}$

Thus, the length of side $QR$ is approximately 9.8 cm, rounded to 1 decimal place.

Do you have any questions or would you like more details on this solution?

Here are some related questions to explore further:

1. What is the significance of the Pythagorean theorem in different contexts?
2. How would the calculation change if we were dealing with a non-right triangle?
3. Can we solve for the angle $P$ using trigonometric ratios?
4. How would you apply Pythagoras’ theorem in three-dimensional problems?
5. What are some common mistakes to avoid when applying the Pythagorean theorem?

Tip: Always double-check that the triangle you're working with is a right triangle before applying the Pythagorean theorem.