https://file.aiquickdraw.com/mathbot/file/1725353592610ns12g1eq.jpg

A playground is shaped like a right-angled triangle.

The dimensions of the catheters are given in meters on the drawing.

How many meters long is the side 
 ?
Answer: 

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.

Discover how to find the length of a side in a right-angled triangle using the Pythagorean theorem. This problem involves a playground shaped like a right-angled triangle with given dimensions of the legs. Suitable for Grades 7-9.

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