To find the length of \( x \) in the big triangle, we can use the property of similar triangles. Assuming that the two triangles are similar (which is implied by the problem), the ratios of the corresponding side lengths of the triangles will be equal.
From the problem, we have:
- Small triangle sides: \( 11.4 \) inches and \( 18 \) inches
- Big triangle sides: \( x \) inches and \( 23.4 \) inches
The ratio of the sides of the large triangle to the small triangle can be expressed as:
\[ \frac{x}{11.4} = \frac{23.4}{18} \]
Now, we can calculate the right side of the equation:
\[ \frac{23.4}{18} = 1.3 \]
Now, we substitute back into the equation:
\[ \frac{x}{11.4} = 1.3 \]
To solve for \( x \), we multiply both sides by \( 11.4 \):
\[ x = 11.4 \times 1.3 \]
Now calculate \( x \):
\[ x = 11.4 \times 1.3 = 14.82 \]
Thus, the length of \( x \) is:
\[ \boxed{14.82} \text{ inches} \]