To calculate the length of $QR$, we can use the Pythagorean theorem, which states:

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

Here:

• $c$ is the hypotenuse ($PQ$) with a length of $7 \, \text{cm}$,
• $a$ is $PR$ with a length of $3 \, \text{cm}$,
• $b$ is $QR$, which we need to find.

Step-by-Step Calculation:

1. Substitute the values of $a$ and $c$ into the formula: $7^2 = 3^2 + QR^2$

2. Calculate $7^2$ and $3^2$: $49 = 9 + QR^2$

3. Rearrange to solve for $QR^2$: $QR^2 = 49 - 9 = 40$

4. Find $QR$ by taking the square root of $40$: $QR = \sqrt{40} \approx 6.3 \, \text{cm}$

Final Answer:

The length of $QR$ is 6.3 cm (to 1 decimal place).

Would you like further details or explanation? Here are 5 related questions to explore:

1. What is the significance of the Pythagorean theorem in different types of triangles?
2. How can you confirm whether a triangle is a right triangle based on side lengths?
3. What are some real-life applications of the Pythagorean theorem?
4. How can you use the Pythagorean theorem to find the hypotenuse instead of a leg?
5. What happens if the triangle is not right-angled? What method would you use then?

Tip:

Always double-check whether the triangle is right-angled before applying the Pythagorean theorem!