Question

consider the enlargement of the parallelogram.
set up a proportion to solve for the missing measure of the original parallelogram.
which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram?
what is the second step in solving the proportion?
what is the value of the missing measure?

Explanation:

Step1: Set up proportion

Since the parallelograms are similar, the ratios of corresponding sides are equal. The side \(3\frac{1}{4}\) ft (original) corresponds to 8 ft (enlarged), and \(x\) ft (original) corresponds to 6 ft (enlarged). The proportion is \(\frac{3\frac{1}{4}}{8}=\frac{x}{6}\).

Step2: Convert mixed number to improper fraction

\(3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4}\). So the proportion becomes \(\frac{\frac{13}{4}}{8}=\frac{x}{6}\), which simplifies to \(\frac{13}{4\times8}=\frac{x}{6}\) or \(\frac{13}{32}=\frac{x}{6}\).

Step3: Cross - multiply

Cross - multiplying gives \(32x=13\times6\).

Step4: Solve for \(x\)

\(32x = 78\), then \(x=\frac{78}{32}=\frac{39}{16}=2\frac{7}{16}\) ft.

Answer:

The value of the missing measure \(x\) is \(2\frac{7}{16}\) ft.