To find the value of \( x \) in the two similar triangles, we can set up a proportion based on the lengths of the corresponding sides.
Let's assume the side lengths of the first triangle are \( 39.6 \) inches and \( 26.4 \) inches, while in the second triangle, the corresponding side is \( 11.1 \) inches, and \( x \) is the unknown side length.
Since the triangles are similar, we can set up the following proportion:
\[ \frac{39.6}{x} = \frac{26.4}{11.1} \]
Now, we can cross-multiply to solve for \( x \):
\[ 39.6 \cdot 11.1 = 26.4 \cdot x \]
Calculating \( 39.6 \cdot 11.1 \):
\[ 39.6 \times 11.1 = 439.56 \]
Thus, we have:
\[ 439.56 = 26.4 \cdot x \]
Now, we divide both sides by \( 26.4 \) to isolate \( x \):
\[ x = \frac{439.56}{26.4} \]
Calculating \( \frac{439.56}{26.4} \):
\[ x \approx 16.65 \]
Rounding to the nearest tenth:
\[ x \approx 16.7 \]
Therefore, the value of \( x \) is approximately 16.7 inches.