To solve for \( x \) in the similar triangles, we can set up a proportion based on the corresponding sides of the triangles.
Letβs use the lengths of the sides provided:
- For the triangles, we have:
- One side from the first triangle: 35 inches
- Corresponding side from the second triangle: 23.2 inches
- The unknown side in the second triangle: \( x \)
- Corresponding side in the first triangle: 10.2 inches
According to the property of similar triangles, the ratios of the corresponding sides are equal:
\[ \frac{35}{23.2} = \frac{x}{10.2} \]
Now, we can cross-multiply to solve for \( x \):
\[ 35 \cdot 10.2 = 23.2 \cdot x \]
Calculating \( 35 \cdot 10.2 \):
\[ 35 \cdot 10.2 = 357 \]
So our equation now looks like:
\[ 357 = 23.2 \cdot x \]
To isolate \( x \), divide both sides by 23.2:
\[ x = \frac{357}{23.2} \]
Calculating \( \frac{357}{23.2} \):
\[ x \approx 15.4 \]
Thus, rounding to the nearest tenth:
\[ \boxed{15.4} \] inches.