To solve for \( x \) in the similar triangles, we can set up a proportion based on the corresponding sides of the triangles.
Given:
- Triangle 1: \( 30.7 \) inches (corresponds to \( 22.1 \) inches)
- Triangle 2: \( x \) inches (corresponds to \( 12.2 \) inches)
We can set up the following proportion:
\[ \frac{30.7}{22.1} = \frac{x}{12.2} \]
Now we can cross-multiply:
\[ 30.7 \times 12.2 = 22.1 \times x \]
Calculating the left side:
\[ 30.7 \times 12.2 = 374.54 \]
So now we have:
\[ 374.54 = 22.1 \times x \]
Next, we can solve for \( x \):
\[ x = \frac{374.54}{22.1} \]
Calculating \( x \):
\[ x \approx 16.9 \]
Thus, the value of \( x \) is approximately:
\[ \boxed{16.9} \text{ inches} \]
Make sure to round to the nearest tenth as asked, which we've done.