To find the value of \( x \) as the shortest leg of a right triangle using the geometric mean, we can use the formula that relates the legs of a right triangle and the altitude drawn from the right angle to the hypotenuse.
In this case, if we assume that the two legs of the right triangle are 3 and 5, the geometric mean \( x \) can be found using the formula:
\[ x = \sqrt{a \cdot b} \]
where \( a = 3 \) and \( b = 5 \).
Calculating this:
\[ x = \sqrt{3 \cdot 5} = \sqrt{15} \]
Now we will find the approximate decimal value of \( \sqrt{15} \):
\[ \sqrt{15} \approx 3.872 \]
Rounding this to the nearest tenth, we get:
\[ x \approx 3.9 \]
Thus, the value of \( x \) is approximately 3.9.
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