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using pythagoras therom, calculate the value of x give your answer in cm and give any decimal answers to 1 d.p.

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!

Using Pythagoras' theorem, calculate the value of x. Give your answer in cm and round any decimal answers to 1 decimal place.

Learn how to calculate the hypotenuse of a right-angled triangle using Pythagoras' Theorem. Given two sides of 12 cm and 16 cm, this step-by-step solution will help you solve for x. Suitable for students in Grades 6-9.

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