To find the length of \( x \) in the second triangle, it appears we're trying to find a relationship between the two triangles involving their sides. It seems you might be using the concept of proportion based on similar triangles.
According to the dimensions given:
- First triangle: Side \( a = 11.4 \), Side \( b = 18 \)
- Second triangle: Side \( a = x \), Side \( b = 23.4 \)
We can set up a proportion based on the similarity of the triangles:
\[ \frac{a_1}{b_1} = \frac{a_2}{b_2} \]
Substituting the known values:
\[ \frac{11.4}{18} = \frac{x}{23.4} \]
To find \( x \), cross-multiply:
\[ 11.4 \times 23.4 = 18 \times x \]
Calculating the left side:
\[ 11.4 \times 23.4 = 267.96 \]
Now we set up the equation:
\[ 267.96 = 18x \]
Now, solve for \( x \):
\[ x = \frac{267.96}{18} \approx 14.88 \]
Rounding to the nearest hundredth, the length of \( x \) is:
\[ \boxed{14.88} \]