To solve for $x$ in the given right-angled triangle using Pythagoras' Theorem, we can use the formula:

$x^2 = a^2 + b^2$

Where:

• $x$ is the hypotenuse (the side opposite the right angle),
• $a$ and $b$ are the other two sides.

In the diagram:

• $a = 12 \, \text{cm}$,
• $b = 16 \, \text{cm}$,
• $x$ is the hypotenuse we need to find.

Step-by-step calculation:

$x^2 = 12^2 + 16^2$ $x^2 = 144 + 256$ $x^2 = 400$ $x = \sqrt{400} = 20 \, \text{cm}$

Therefore, the value of $x$ is 20 cm.

Would you like more details or further explanations on any step?

Here are five related questions to expand your understanding:

1. What happens if one of the side lengths changes? How does it affect the hypotenuse?
2. How can Pythagoras' Theorem be used in three-dimensional shapes?
3. Can you apply Pythagoras’ Theorem to non-right triangles?
4. What are the properties of right-angled triangles?
5. How would you solve for an unknown leg of the triangle if the hypotenuse is given?

Tip: Remember, Pythagoras' Theorem only applies to right-angled triangles, so always check that first before using the formula!