To find the length of \( x \) in the pair \( (11.4 \text{ in}, 18 \text{ in}) \) corresponding to the second pair \( (x, 23.4 \text{ in}) \), we can use the property of proportions.
We set up the proportion:
\[ \frac{11.4}{18} = \frac{x}{23.4} \]
Now we can cross-multiply to solve for \( x \):
\[ 11.4 \cdot 23.4 = 18 \cdot x \]
Calculating the left side:
\[ 11.4 \times 23.4 = 267.96 \]
So, we have:
\[ 267.96 = 18x \]
Now, divide both sides by 18:
\[ x = \frac{267.96}{18} \]
Calculating that gives:
\[ x \approx 14.88 \]
Thus, the length of \( x \) to the nearest hundredth is:
\[ \boxed{14.88} \]