To set up a proportion to solve for the missing measure of the original parallelogram, we will compare the side lengths of the smaller parallelogram to the side lengths of the larger parallelogram.
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First, we note the side lengths of the smaller parallelogram: one side is \( \frac{1}{3} \) foot, and the other side is \( x \) feet. The side lengths of the larger parallelogram are 8 feet and 6 feet.
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We will establish a proportional relationship. The side of the original (smaller) parallelogram that corresponds to the 6 ft side of the enlarged parallelogram will be the side \( x \). This is because both parallelograms have their corresponding sides proportional to each other.
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Therefore, we set up the proportion as follows, with \( x \) corresponding to the enlarged side of 6 ft:
\[ \frac{x}{6} = \frac{\frac{1}{3}}{8} \]
- The next step in solving the proportion is to cross-multiply:
\[ x \cdot 8 = 6 \cdot \frac{1}{3} \]
- This simplifies to:
\[ 8x = 2 \]
- Now, solving for \( x \) involves dividing both sides by 8:
\[ x = \frac{2}{8} = \frac{1}{4} \]
Therefore, the value of the missing measure \( x \) in the original parallelogram is \( \frac{1}{4} \) feet.
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