The problem presented in the image is a right triangle where we need to find the length of the hypotenuse, $x$, given that the other two sides are 6 and 8.

To solve this, we can use the Pythagorean theorem, which states that in a right triangle:

$x^2 = a^2 + b^2$

where $a$ and $b$ are the lengths of the legs of the triangle, and $x$ is the hypotenuse. In this case:

$x^2 = 6^2 + 8^2$ $x^2 = 36 + 64 = 100$ $x = \sqrt{100} = 10$

Thus, the correct answer is $\boxed{x = 10}$, which corresponds to option C.

Would you like further details or have any questions about this?

Here are five related questions to expand your understanding:

1. How do we apply the Pythagorean theorem to different types of triangles?
2. What happens if one of the legs is missing and we know the hypotenuse?
3. How can we find the area of the triangle using the given sides?
4. What other methods can be used to verify the result of a right triangle?
5. How does the Pythagorean theorem extend to three dimensions?

Tip: Always check that the triangle is a right triangle before applying the Pythagorean theorem!