To find the value of \( x \) using the geometric mean in a right triangle configuration where the legs are given as 3 and 5, we apply the formula for the geometric mean. In a right triangle, if \( a \) and \( b \) are the lengths of the legs, the geometric mean \( x \) of the legs can be calculated as follows:
\[ x = \sqrt{a \cdot b} \]
In this case:
\[ a = 3 \quad \text{and} \quad b = 5 \]
So:
\[ x = \sqrt{3 \cdot 5} = \sqrt{15} \]
Calculating \( \sqrt{15} \):
\[ \sqrt{15} \approx 3.872 \]
Rounding to the nearest tenth gives:
\[ x \approx 3.9 \]
From the options provided (4.9, 8, 2.8, 15), none of them matches exactly, but if you were asking about the side lengths of the triangle, you might be looking for a solution that identifies \( x \) (the shortest leg).
If we interpret the problem indicating that \( x \) represents the geometric mean between the segment lengths and apply that, the answer closest to our calculation and is considered in the geometric mean as \( x \geq 3 \) would be:
\[ \text{The shortest leg doesn't strictly match any option but is approximately: } 3.9 \]
If you are looking at something else or if the geometric mean should yield integer results based on conditions or specific figures defined in the relationships, please clarify so we can refine the output.
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