To find the missing side length \( x \) in the two similar figures using proportions, we can set up the proportion based on corresponding sides.
Given the sides of shape one are 3.25 and 4.23, and the sides of shape two are 13 and \( x \):
\[ \frac{3.25}{13} = \frac{4.23}{x} \]
Now, cross-multiply to solve for \( x \):
\[ 3.25 \cdot x = 4.23 \cdot 13 \]
Calculating \( 4.23 \cdot 13 \):
\[ 4.23 \cdot 13 = 55.99 \]
Now substitute back into the equation:
\[ 3.25x = 55.99 \]
Next, solve for \( x \):
\[ x = \frac{55.99}{3.25} \]
Calculating \( \frac{55.99}{3.25} \):
\[ x \approx 17.23 \]
Thus, the missing side length \( x \) is approximately 17.23.
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