To find the missing side length \( x \) in the two similar triangles using proportions, we can set up a proportion based on the corresponding sides.
The corresponding sides of the triangles give us the following relationship:
\[ \frac{13 \text{ yards}}{3.25 \text{ yards}} = \frac{x}{4.23 \text{ yards}} \]
Now, we can cross-multiply to solve for \( x \):
\[ 13 \cdot 4.23 = 3.25 \cdot x \]
Calculating the left side:
\[ 13 \cdot 4.23 = 55.99 \]
Now the equation is:
\[ 55.99 = 3.25x \]
Next, divide both sides by 3.25 to isolate \( x \):
\[ x = \frac{55.99}{3.25} \approx 17.23 \]
But it seems that the answer choices provided are different. Let's calculate the ratio:
Calculating actual ratio values:
- Find the ratio of the corresponding sides:
\[ \text{Ratio} = \frac{13}{3.25} = 4 \]
- Now use this ratio to find \( x \):
If \( y \) corresponds to \( 4.23 \), setting up:
\[ \frac{x}{4.23} = 4 \]
Thus,
\[ x = 4 \cdot 4.23 = 16.92 \]
So, the correct answer is 16.92 yards.