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To calculate the length of \( XY \) using Pythagoras' Theorem, we can follow these steps:

### Given:
- Triangle \( WXY \) is a right triangle (with the right angle at \( W \)).
- \( WZ = 4.2 \, \text{cm} \) (the height of the triangle).
- \( XY = ZY - WZ = 4 \, \text{cm} - 2 \, \text{cm} = 2 \, \text{cm} \) (this forms the base of the triangle \( WXY \)).
- \( WX = 4.2 \, \text{cm} \) (this is given as one of the sides).

### Pythagoras’ Theorem:
For a right-angled triangle:
\[
XY^2 = WX^2 + WY^2
\]
We already have the following:
- \( WX = 4.2 \, \text{cm} \)
- \( WY = 2 \, \text{cm} \)

Now, let’s apply the formula:

\[
XY^2 = (4.2)^2 + (2)^2
\]

Let me calculate that for you.The length of \( XY \) is approximately \( 4.7 \, \text{cm} \) when rounded to 1 decimal place.

Would you like more details, or do you have any other questions?

Here are 5 related questions for further exploration:
1. How is Pythagoras' theorem applied in 3D geometry?
2. How would the solution change if the triangle were not a right triangle?
3. Can Pythagoras' theorem be used with coordinates in a coordinate plane?
4. How can you use Pythagoras' theorem to find the diagonal of a rectangle?
5. What real-world applications involve the use of Pythagoras' theorem?

**Tip:** Pythagoras' theorem is only applicable in right-angled triangles. Make sure the triangle fits this condition before applying the formula!

Using Pythagoras' theorem, calculate the length of XY. Give your answer to 1 d.p.

Learn how to calculate the length of XY using Pythagoras' theorem in a right-angled triangle. Given the sides WX = 4.2 cm and WY = 2 cm, use Pythagoras' theorem to solve for XY. Suitable for Grade 6-7 students.

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