When two shapes are similar, the ratios of their corresponding lengths, perimeters, and areas can be determined based on the ratio of their corresponding side lengths.
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Ratio of side lengths: The ratio of the side lengths of the two similar parallelograms is equal to the ratio of any two corresponding lengths. Here, if we take the side length from the first parallelogram as 6 inches and the corresponding side length from the second parallelogram as 24 inches, the ratio is: \[ \text{Ratio of side lengths} = \frac{6}{24} = \frac{1}{4}. \]
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Ratio of perimeter: The perimeter of similar shapes is also in the same ratio as their side lengths. Therefore, the ratio of the perimeters of the two parallelograms will similarly be: \[ \text{Ratio of perimeters} = \frac{6}{24} = \frac{1}{4}. \]
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Ratio of areas: The ratio of the areas of similar shapes is equal to the square of the ratio of their corresponding side lengths. Thus, we square our side length ratio: \[ \text{Ratio of areas} = \left(\frac{1}{4}\right)^2 = \frac{1}{16}. \]
To summarize:
- The ratio of side lengths is \(\frac{1}{4}\).
- The ratio of perimeters is \(\frac{1}{4}\).
- The ratio of areas is \(\frac{1}{16}\).
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