https://file.aiquickdraw.com/mathbot/file/1728658927117epp2n2g4.jpg

The problem presented in the image shows a right triangle with one leg of length 7 and another leg of length 24. We are tasked with finding the length of the third side, which is the hypotenuse, since the triangle contains a right angle.

We can use the **Pythagorean Theorem**, which states:

\[
a^2 + b^2 = c^2
\]

Where:
- \( a \) and \( b \) are the lengths of the legs (7 and 24, respectively),
- \( c \) is the length of the hypotenuse (the unknown side we are trying to find).

Let's calculate:

\[
7^2 + 24^2 = c^2
\]

\[
49 + 576 = c^2
\]

\[
625 = c^2
\]

Now, take the square root of both sides:

\[
c = \sqrt{625} = 25
\]

Therefore, the length of the hypotenuse is **25**.

Would you like further details or explanations on this? Here are some related questions you can explore:

1. How does the Pythagorean Theorem apply to non-right triangles?
2. What are some real-world applications of the Pythagorean Theorem?
3. How can you calculate the area of a right triangle given its sides?
4. What is the Pythagorean Theorem's role in trigonometry?
5. How would you calculate the length of a side if the hypotenuse and one leg are given?

**Tip**: When solving for unknown sides in right triangles, always confirm if the triangle is a right triangle before applying the Pythagorean Theorem!

Find the length of the third side of a right triangle with legs of 7 and 24. If necessary, round to the nearest tenth.

In this problem, we use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle with legs measuring 7 and 24. This step-by-step solution is suitable for students in grades 7-10.

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