Since the two quadrilaterals are similar, the ratios of their corresponding side lengths are equal.
Given:
- Smaller quadrilateral sides: 2 and 5
- Larger quadrilateral sides: 3.6 and \( x \)
We can set up a ratio using one pair of corresponding sides:
\[ \frac{2}{3.6} = \frac{5}{x} \]
To solve for \( x \), we will cross-multiply:
\[ 2x = 5 \cdot 3.6 \]
Calculating \( 5 \cdot 3.6 \):
\[ 5 \cdot 3.6 = 18 \]
So we have:
\[ 2x = 18 \]
Now, divide both sides by 2:
\[ x = \frac{18}{2} = 9 \]
Thus, the value of \( x \) is \( \boxed{9} \).