Question: Calculate the length of $QR$. Give your answer to 1 d.p. Triangle $PQR$, right angle at $P$, with $PQ = 7$ cm, $PR = 3$ cm, and $QR$ is the slanted side to be calculated; position\_hint: center
1. **State the problem:** We need to find the length of the hypotenuse $QR$ in right triangle $PQR$ where the right angle is at $P$. The legs are $PQ = 7$ cm and $PR = 3$ cm.
2. **Formula used:** In a right triangle, the Pythagorean theorem states:
$$QR^2 = PQ^2 + PR^2$$
This means the square of the hypotenuse equals the sum of the squares of the other two sides.
3. **Calculate the squares:**
$$PQ^2 = 7^2 = 49$$
$$PR^2 = 3^2 = 9$$
4. **Sum the squares:**
$$QR^2 = 49 + 9 = 58$$
5. **Find $QR$ by taking the square root:**
$$QR = \sqrt{58}$$
6. **Calculate the decimal value:**
$$QR \approx 7.6157$$
7. **Round to 1 decimal place:**
$$QR \approx 7.6$$
**Final answer:** The length of $QR$ is approximately $7.6$ cm.