The diagram appears to involve a right triangle where we are tasked to solve for the variable $x$, which represents the hypotenuse of the triangle.

Given:

1. One leg = $6$ (adjacent to the right angle).
2. The other leg = $12$ (opposite to the right angle).

To solve for $x$, we use Pythagoras' theorem:

$x^2 = 6^2 + 12^2$

Step-by-step Solution:

1. Compute the squares of the two legs: $6^2 = 36, \quad 12^2 = 144$

2. Add the squares: $x^2 = 36 + 144 = 180$

3. Solve for $x$ by taking the square root: $x = \sqrt{180} = \sqrt{36 \cdot 5} = 6\sqrt{5}$

   Approximating numerically: $x \approx 13.42$

Final Answer:

$x = 6\sqrt{5} \quad \text{or approximately } 13.42$

Let me know if you'd like further clarification or if you have more questions.

Related Questions:

1. What is the derivation of the Pythagorean theorem?
2. Can you apply this theorem in non-right triangles?
3. How do you simplify square roots like $\sqrt{180}$?
4. What are the properties of right triangles used in this calculation?
5. How does trigonometry relate to solving for unknown sides?

Tip:

Always double-check your calculations when solving square roots, especially when approximating values!