To find the value of \( x \) using the geometric mean in a right triangle, we can apply the geometric mean theorem. This theorem states that in a right triangle, the altitude to the hypotenuse creates two smaller right triangles that are similar to the original triangle and to each other.
According to the theorem:
\[ x^2 = a \cdot b \]
where:
- \( x \) is the length of the altitude from the vertex opposite the hypotenuse to the hypotenuse,
- \( a \) and \( b \) are the lengths of the segments of the hypotenuse created by the foot of the altitude.
To solve for \( x \), we need the values of \( a \) and \( b \), which are the segments of the hypotenuse.
If you provide the lengths of \( a \) and \( b \), I can help you calculate \( x \). Alternatively, if you are looking for a specific answer based on multiple choice options given in your question, please check the values you have for \( a \) and \( b \) and apply the formula, then select the closest answer rounded to the nearest tenth.
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