To determine the value of \( x \) in the similar triangles, we'll use the property of similar triangles that states the ratios of corresponding sides are equal.
Let's denote the sides of the triangles:
- For the larger triangle, the sides are 33.1 inches and 20.9 inches.
- For the smaller triangle, the sides are 17 inches and \( x \).
Setting up the proportion using the corresponding sides, we have:
\[ \frac{33.1}{17} = \frac{20.9}{x} \]
Now, we cross-multiply to solve for \( x \):
\[ 33.1 \cdot x = 20.9 \cdot 17 \]
Calculating \( 20.9 \cdot 17 \):
\[ 20.9 \cdot 17 = 355.3 \]
Now we have:
\[ 33.1x = 355.3 \]
Next, we solve for \( x \) by dividing both sides by 33.1:
\[ x = \frac{355.3}{33.1} \approx 10.7 \]
Rounding to the nearest tenth, we find:
\[ x \approx 10.7 \text{ inches} \]
Thus, the value of \( x \) is approximately 10.7 inches.
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