The given image shows a right-angled triangle $PQR$ with a right angle at $P$. We are given the following information:

• $PR = 3 \, \text{cm}$ (one leg),
• $PQ = 8 \, \text{cm}$ (the other leg).

We need to find the length of $QR$ (the hypotenuse).

To calculate this, we can apply the Pythagorean theorem, which states that:

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

Where:

• $c$ is the length of the hypotenuse (in this case, $QR$),
• $a$ and $b$ are the lengths of the other two sides (here $PQ$ and $PR$).

Substitute the given values:

$QR^2 = PQ^2 + PR^2$

$QR^2 = 8^2 + 3^2$

$QR^2 = 64 + 9 = 73$

Now, solve for $QR$:

$QR = \sqrt{73} \approx 8.54 \, \text{cm}$

Thus, the length of $QR$ is approximately 8.54 cm.

Do you need further details or clarifications on this? Here are some related questions:

1. What is the formula for the Pythagorean theorem?
2. How can the Pythagorean theorem be used in non-right-angled triangles?
3. How do you approximate square roots to specific decimal places?
4. What other methods can be used to find the hypotenuse of a triangle?
5. How do you identify the legs and hypotenuse in a right triangle?

Tip: Always ensure that you are using the correct sides of the triangle for the Pythagorean theorem—two legs for $a$ and $b$, and the hypotenuse for $c$.