To find the length of \( x \) in the second triangle that corresponds to the first triangle, we will use the concept of similar triangles. The triangles are similar, meaning that the ratios of their corresponding sides are equal.
Given the sides of the first triangle are 9.4 in and 16 in, and the sides of the second triangle are \( x \) and 22.4 in, we can set up the proportion:
\[ \frac{9.4}{16} = \frac{x}{22.4} \]
Now we can solve for \( x \):
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Cross-multiply: \[ 9.4 \times 22.4 = 16 \times x \]
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Calculate \( 9.4 \times 22.4 \): \[ 9.4 \times 22.4 = 210.56 \]
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Now we have: \[ 210.56 = 16 \times x \]
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Divide both sides by 16 to find \( x \): \[ x = \frac{210.56}{16} = 13.160 \]
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Rounding this to the nearest hundredth gives: \[ x \approx 13.16 \]
Thus, the length of \( x \) is \( \boxed{13.16} \) inches.
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