The triangle in the image is a right-angled triangle with the two shorter sides (the legs or catheti) measuring 5 meters and 12 meters. The side labeled $x$ is the hypotenuse, which we need to find.

To find the length of the hypotenuse $x$, we can use the Pythagorean theorem, which states: $x^2 = a^2 + b^2$ where $a$ and $b$ are the lengths of the two legs.

Substituting the given values: $x^2 = 5^2 + 12^2$ $x^2 = 25 + 144$ $x^2 = 169$ $x = \sqrt{169}$ $x = 13 \text{ meters}$

So, the length of the hypotenuse $x$ is 13 meters.

Would you like any further explanation on this? Here are some related questions you might find helpful:

1. How do you apply the Pythagorean theorem in non-right triangles?
2. What are some real-life applications of the Pythagorean theorem?
3. How can you determine if a triangle is a right triangle using side lengths?
4. How do you calculate the area of this triangle?
5. What are the properties of a 5-12-13 triangle?

Tip: The Pythagorean theorem only applies to right-angled triangles. If the triangle is not right-angled, you would need to use other methods like the Law of Cosines.