The image shows a right triangle with legs of length 12 and 10. We need to find the length of the hypotenuse $x$.

We can use the Pythagorean Theorem, which states that for a right triangle:

$a^2 + b^2 = c^2$

where:

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

Given:

• $a = 12$,
• $b = 10$,
• $c = x$ (the unknown hypotenuse).

Let's calculate the value of $x$.

$x^2 = 12^2 + 10^2 = 144 + 100 = 244$

Taking the square root of both sides:

$x = \sqrt{244} \approx 15.62$

Thus, the length of the hypotenuse $x$ is approximately 15.62 units.

Would you like more details, or do you have any questions about the process?

Here are some related questions you might explore:

1. How does the Pythagorean Theorem change if the triangle is not a right triangle?
2. How do you find the area of this triangle using the known sides?
3. What is the perimeter of the triangle after finding the hypotenuse?
4. How can you verify that this is a right triangle using trigonometry?
5. Can the Pythagorean Theorem be applied in three-dimensional geometry?

Tip: The Pythagorean Theorem is only applicable in right-angled triangles, and it helps to confirm the type of triangle before applying it.