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!