To solve for the missing side length \(x\) in similar triangles, we can set up the equivalent ratios based on the information given.
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Set up equivalent ratios: Since you’ve provided \(4/x\), we need another side length from the second triangle. For example, let’s assume the corresponding side length from the second triangle is \(9\) (this is a placeholder; you can replace it as needed based on the actual problem).
The ratio would then be: \[ \frac{4}{x} = \frac{9}{y} \] (where \(y\) is the length of the side in the second triangle corresponding to \(x\)).
However, if we know or defined the other side in the second triangle or context, our equation could look like: \[ \frac{4}{x} = \frac{9}{36} \] (for a specific case).
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Cross Multiply: Now, cross-multiply to find the relationship: \[ 4 \cdot 36 = 9 \cdot x \] So you would get: \[ 144 = 9x \]
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Solve for \(x\): Now, isolate \(x\): \[ x = \frac{144}{9} \] Simplifying gives: \[ x = 16 \text{ miles} \]
Now, let's summarize the answers you could fill in:
- Equivalent ratios: \( \frac{4}{x} = \frac{9}{36} \)
- Cross multiply: \( 144 = 9x \)
- Solve for \(x\): \( x = 16 \text{ miles} \)
Make sure to adapt any specific numbers based on the actual ratios of your triangles!
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