Solution:

We are given a right-angled triangle $\triangle PQR$ with the following sides:

• $PQ = 7 \, \text{cm}$ (the hypotenuse),
• $PR = 3 \, \text{cm}$ (one leg),
• $QR$ (the other leg, which we need to calculate).

Using Pythagoras' Theorem: $PQ^2 = PR^2 + QR^2$

Substituting the given values: $7^2 = 3^2 + QR^2$

Simplifying: $49 = 9 + QR^2$

Solving for $QR^2$: $QR^2 = 49 - 9$ $QR^2 = 40$

Taking the square root: $QR = \sqrt{40} \approx 6.3 \, \text{cm} \, \text{(to 1 decimal place)}.$

Final Answer:

The length of $QR$ is 6.3 cm.

Would you like further clarification or a step-by-step breakdown of any part?

Related Questions:

1. How is Pythagoras' Theorem derived?
2. What are the common applications of Pythagoras' Theorem in real life?
3. How do you determine which side is the hypotenuse in a right triangle?
4. What is the difference between exact values and rounded answers in geometry?
5. How would the calculation change if the hypotenuse were unknown?

Tip:

Always identify the hypotenuse (longest side) first when applying Pythagoras' Theorem!