To solve for \( x \) in the similar triangles, we can use the property that the ratios of corresponding sides of similar triangles are equal.
Given:
- Larger triangle sides: 33.1 inches and 17 inches
- Smaller triangle sides: 20.9 inches and \( x \)
We can set up a proportion based on the corresponding sides:
\[ \frac{33.1}{20.9} = \frac{17}{x} \]
Now, we will cross-multiply to solve for \( x \):
\[ 33.1 \times x = 20.9 \times 17 \]
Calculating \( 20.9 \times 17 \):
\[ 20.9 \times 17 = 355.3 \]
Now we can plug that back into our equation:
\[ 33.1x = 355.3 \]
Now, divide both sides by 33.1 to isolate \( x \):
\[ x = \frac{355.3}{33.1} \]
Calculating \( \frac{355.3}{33.1} \):
\[ x \approx 10.7 \]
So, the value of \( x \) rounded to the nearest tenth is:
\[ \boxed{10.7} \text{ inches} \]