Since the two quadrilaterals are similar, their corresponding sides are proportional.
We know the following measurements:
- In the small quadrilateral, one side measures 2, and the opposite side measures 5.
- In the big quadrilateral, the corresponding side to 2 measures 3.6, and the corresponding side to 5 measures \( x \).
We can set up the proportion based on the corresponding sides:
\[ \frac{2}{5} = \frac{3.6}{x} \]
To solve for \( x \), we cross-multiply:
\[ 2x = 5 \times 3.6 \]
Calculating the right side:
\[ 5 \times 3.6 = 18 \]
Now we have:
\[ 2x = 18 \]
Next, we solve for \( x \) by dividing both sides by 2:
\[ x = \frac{18}{2} = 9 \]
Thus, the value of \( x \) is \( \boxed{9} \).
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