The given triangle in the image is a right triangle, as indicated by the small square at the corner. Two sides are provided: one leg is 24, and the hypotenuse is 26. We need to find the length of the third side, which is the other leg.

Using the Pythagorean theorem: $a^2 + b^2 = c^2$ where:

• $a$ and $b$ are the legs of the triangle,
• $c$ is the hypotenuse.

Here, one leg $a = 24$ and the hypotenuse $c = 26$. Let's solve for the missing leg $b$.

$24^2 + b^2 = 26^2$ $576 + b^2 = 676$ $b^2 = 676 - 576$ $b^2 = 100$ $b = \sqrt{100} = 10$

Thus, the length of the third side is 10.

Let me know if you would like further details or have any other questions!

Here are five follow-up questions to expand on this concept:

1. How does the Pythagorean theorem apply in non-right triangles?
2. Can the sides of any triangle form a right triangle?
3. How do you calculate the area of this triangle now that you know all sides?
4. What are some real-world applications of the Pythagorean theorem?
5. How can you check whether a triangle is right-angled based on side lengths?

Tip: For future geometry problems, memorizing common Pythagorean triples (like 3-4-5 or 5-12-13) can help quickly identify side lengths.