Question

Consider the enlargement of the parallelogram.

A smaller parallelogram with side lengths one-third foot and x feet. A larger parallelogram with side lengths 8 feet and 6 feet.

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?

Answer 1

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.

1. 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.

2. 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.

3. Therefore, we set up the proportion as follows, with \( x \) corresponding to the enlarged side of 6 ft:

\[
\frac{x}{6} = \frac{\frac{1}{3}}{8}
\]

4. The next step in solving the proportion is to cross-multiply:

\[
x \cdot 8 = 6 \cdot \frac{1}{3}
\]

5. This simplifies to:

\[
8x = 2
\]

6. 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.