Question

1. the two parallelograms below are similar.

what is the length in inches of \\( \overline { p q } \\)?
a. 40 in.
b. 34 in.
c. 38 in.
d. 14 in.

Explanation:

Step1: Set up the proportion

Since the two parallelograms are similar, the ratios of their corresponding sides are equal. Let the length of \(PQ\) be \(x\). We have the proportion \(\frac{12}{30}=\frac{16}{x}\).

Step2: Cross - multiply

Cross - multiplying gives us \(12x = 30\times16\).

Step3: Solve for \(x\)

First, calculate \(30\times16 = 480\). Then, \(x=\frac{480}{12}\).

Step4: Calculate the value of \(x\)

\(x = 40\).

Answer:

A. 40 in.