Question

1. the ratio of the perimeters is 8 : 5.

Explanation:

Step1: Set up proportion

For similar - shaped figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths. Let the side lengths of the two similar parallelograms be \(x\) and \(16\), and the ratio of the perimeters is \(8:5\). So we can set up the proportion \(\frac{x}{16}=\frac{8}{5}\).

Step2: Cross - multiply and solve for \(x\)

Cross - multiplying gives us \(5x = 16\times8\). Then \(5x=128\), and \(x=\frac{128}{5}=25.6\).

Answer:

\(x = 25.6\)