This is a right-angled triangle problem that applies Pythagoras' theorem. The equation is:

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

where $c$ is the hypotenuse (longest side). From the image:

• Hypotenuse ($c$) = 41 cm
• One side ($b$) = 9 cm
• Unknown side ($a$) needs to be calculated.

Steps to Solve:

1. Start with $a^2 + 9^2 = 41^2$.
2. Simplify $9^2$ and $41^2$: $a^2 + 81 = 1681$
3. Subtract 81 from both sides: $a^2 = 1681 - 81$ $a^2 = 1600$
4. Take the square root of $a^2$: $a = \sqrt{1600}$ $a = 40$

Final Answer:

The unknown side length is $a = 40 \, \text{cm}$.

Would you like further clarification or additional examples?

Related Questions:

1. How is Pythagoras' theorem used in real-world applications?
2. What happens if both non-hypotenuse sides are unknown?
3. How can you verify your answer in a Pythagorean problem?
4. What are the conditions for a triangle to be a right-angled triangle?
5. Can Pythagoras' theorem be extended to non-Euclidean geometry?

Tip:

Always ensure the hypotenuse ($c$) is the largest side when using Pythagoras' theorem.