Calculate the missing lengths and angles in the provided geometric figures.

From , we focus on the left right-angled triangle.
The hypotenuse of this triangle is given as $6 \text{ cm}$.
One leg of this triangle is labeled $x \text{ cm}$.
The vertical leg (height) is marked with the same double dash symbol as $x$, indicating its length is also $x \text{ cm}$.

The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the other two sides ($a$ and $b$): $a^2 + b^2 = c^2$.
In this triangle, $a = x$, $b = x$, and $c = 6$.

Divide both sides by 2:

Take the square root of both sides:

Simplify the square root:

The value of $x$ is: