https://file.aiquickdraw.com/mathbot/file/17293796116255tjv0y74.jpg

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!

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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.

Find the length of the third side of a right triangle with one leg measuring 24 units and the hypotenuse measuring 26 units. Round to the nearest tenth if necessary.

Learn how to find the length of the third side of a right triangle where one leg is 24 units and the hypotenuse is 26 units. Using the Pythagorean theorem, this problem demonstrates key geometry concepts suitable for students in Grades 6-8.

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