To find the length of \(x\) in the second triangle, we need to establish a relationship between the two triangles based on their corresponding sides.
We are given:
- One triangle has sides 11.4 inches and 18 inches.
- The other triangle has sides \(x\) and 23.4 inches.
If we assume that the triangles are similar, we can set up a proportion based on the lengths of the sides:
\[ \frac{x}{23.4} = \frac{11.4}{18} \]
Now, we can solve for \(x\). First, we calculate the ratio on the right:
\[ \frac{11.4}{18} = 0.6333... \quad (\text{approximately } 0.6333) \]
Now we rewrite the proportion:
\[ \frac{x}{23.4} = 0.6333 \]
To solve for \(x\), we cross-multiply:
\[ x = 23.4 \times 0.6333 \]
Calculating that gives:
\[ x \approx 14.85382 \]
Now, rounding this to the nearest hundredth:
\[ x \approx 14.85 \]
Therefore, the length of \(x\) is approximately 14.85 inches.