To find the value of \( x \) using the geometric mean in a triangle, we typically apply the property that states the geometric mean of the two legs of a right triangle is equal to the length of the altitude to the hypotenuse.
However, if we are looking for the geometric mean of two other numbers, we can use the formula for the geometric mean:
\[ x = \sqrt{a \cdot b} \]
where \( a \) and \( b \) are the two known values. In this case, we have 5 and 3.
Let's calculate \( x \):
\[ x = \sqrt{5 \cdot 3} = \sqrt{15} \approx 3.87 \]
Rounding to the nearest tenth gives us approximately 3.9.
However, since none of the given responses match this calculation, there might be more context needed from the original problem regarding the specific method used to derive \( x \).
If you would like, please provide additional details about the triangles or the relationship between the legs and the altitude so that I can help you more accurately. Otherwise, based on the provided options, there might have been a misunderstanding, or we can select 15 which is also the product of 5 and 3, but again, it does not logically fit within geometric mean calculations directly based on the problem context.