To solve for the length of \( x \) in triangle two, we can use the concept of similar triangles, assuming the two triangles are similar based on the given information.
First, we identify the corresponding sides from both triangles:
- In triangle one, the sides are 2 inches and 1.4 inches.
- In triangle two, the corresponding sides are \( x \) inches and 9.6 inches.
Since the triangles are similar, the ratios of the corresponding sides are equal. Therefore, we can set up the following proportion:
\[ \frac{2}{x} = \frac{1.4}{9.6} \]
Now, we can solve for \( x \):
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Cross-multiply to eliminate the fraction: \[ 2 \cdot 9.6 = 1.4 \cdot x \]
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Calculate \( 2 \cdot 9.6 \): \[ 19.2 = 1.4x \]
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Now, divide both sides by 1.4 to isolate \( x \): \[ x = \frac{19.2}{1.4} \]
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Calculate \( \frac{19.2}{1.4} \): \[ x = 13.714285714285714 \] which can be rounded to: \[ x \approx 13.71 \text{ inches} \]
Thus, the length of \( x \) is approximately 13.71 inches.
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