We can solve this problem using Pythagoras' Theorem, which states:

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

Where $c$ is the hypotenuse (the longest side), and $a$ and $b$ are the other two sides of the right triangle.

Given:

• Hypotenuse ($PQ$) = $9 \, \text{cm}$
• One side ($PR$) = $4 \, \text{cm}$
• Unknown side ($QR$) = ?

Rearranging the formula for $QR$:

$QR^2 = PQ^2 - PR^2$

Substituting the values:

$QR^2 = 9^2 - 4^2$

$QR^2 = 81 - 16$

$QR^2 = 65$

Taking the square root:

$QR = \sqrt{65} \approx 8.1 \, \text{cm}$

Final Answer:

The length of $QR$ is approximately 8.1 cm (to 1 decimal place).

Would you like further details or clarifications? 😊

5 Related Questions:

1. How does Pythagoras' theorem work for triangles with different units?
2. Can Pythagoras' theorem be used in three dimensions?
3. What are some real-world applications of this theorem?
4. How do you verify if a triangle is a right triangle using side lengths?
5. How would the calculation change if one of the sides was unknown instead of the hypotenuse?

Tip:

Always check that the triangle is a right triangle before applying Pythagoras' theorem!