To solve for the value of \( x \) using the geometric mean in the context of a right triangle divided by a line drawn from the vertex opposite the hypotenuse to the hypotenuse itself, we can use the formula:
\[ x^2 = a \cdot b \]
where \( a \) and \( b \) are the segments into which the hypotenuse is divided.
In this case:
- One segment is 3 (let's call it \( a \))
- The other segment is 4 (let's call it \( b \))
We can substitute these values into the equation:
\[ x^2 = 3 \cdot 4 \] \[ x^2 = 12 \]
Now, we take the square root of both sides to find \( x \):
\[ x = \sqrt{12} \] \[ x = 2\sqrt{3} \]
Calculating \( 2\sqrt{3} \):
Using the approximate value \( \sqrt{3} \approx 1.732 \):
\[ x \approx 2 \cdot 1.732 \approx 3.464 \]
Now, rounding to the nearest tenth:
\[ x \approx 3.5 \]
Thus, the value of \( x \) rounded to the nearest tenth is:
\[ \boxed{3.5} \]