To find the length of $XY$, we can apply the Pythagorean theorem, which is applicable to right-angled triangles.

Given:

• $XZ = 13 \, \text{cm}$ (the hypotenuse),
• $YZ = 4 \, \text{cm}$ (one of the legs),

we want to calculate $XY$, the other leg.

According to the Pythagorean theorem: $XZ^2 = XY^2 + YZ^2$

Rearrange to solve for $XY$: $XY^2 = XZ^2 - YZ^2$

Substitute the given values: $XY^2 = 13^2 - 4^2$ $XY^2 = 169 - 16$ $XY^2 = 153$

Now, take the square root to find $XY$: $XY = \sqrt{153} \approx 12.4 \, \text{cm}$

Answer:

The length of $XY$ is approximately $12.4 \, \text{cm}$ to 1 decimal place.

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

Here are some related questions:

1. How does the Pythagorean theorem apply to non-right-angled triangles?
2. What other methods can you use to find the length of a side in a right-angled triangle?
3. How would the calculation change if $XZ$ were a different length?
4. Can the Pythagorean theorem be extended to three-dimensional geometry?
5. What are some real-life applications of the Pythagorean theorem?

Tip: When using the Pythagorean theorem, ensure that you identify the hypotenuse (the longest side) correctly, as it’s essential for accurate calculations.