The problem involves finding the length of side $x$ in a right triangle where one leg is 4 units long and the hypotenuse is 12 units long. We can solve for $x$ using the Pythagorean theorem.

The Pythagorean theorem states: $a^2 + b^2 = c^2$ where $a$ and $b$ are the legs of the triangle, and $c$ is the hypotenuse.

Here, $a = 4$, $b = x$, and $c = 12$.

Let's plug in the values: $4^2 + x^2 = 12^2$ $16 + x^2 = 144$

Now, subtract 16 from both sides: $x^2 = 144 - 16$ $x^2 = 128$

Finally, take the square root of both sides to find $x$: $x = \sqrt{128} \approx 11.31$

So, the length of $x$ is approximately 11.31 units when rounded to the nearest hundredth.

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How do you apply the Pythagorean theorem in a right triangle?
2. What is the significance of rounding to the nearest hundredth in measurements?
3. How would you solve for $x$ if the triangle were not a right triangle?
4. What are the possible values for $x$ if the hypotenuse was shorter than 12 units?
5. Can the Pythagorean theorem be applied to non-right triangles?

Tip: When using the Pythagorean theorem, always ensure that the hypotenuse is correctly identified as the side opposite the right angle.