Question

1. determine if the two regular pentagons below are proportional.
2. the distance between home and school is 4.5 miles. on a map it shows the distance to be 9 cm. what is the scale?

Explanation:

Step1: Check the ratio of corresponding sides for pentagons

For the first pair of corresponding sides of the pentagons, find the ratio of the sides of the larger pentagon to the smaller pentagon. $\frac{14}{4}=\frac{7}{2}$.

Step2: Check another pair of corresponding sides

For the second - pair of corresponding sides, calculate the ratio $\frac{98}{28}=\frac{7}{2}$.
Since the ratios of the corresponding sides of the two regular pentagons are equal, they are proportional.

Step3: Calculate the scale for the map problem

Let the scale be $1$ cm represents $x$ miles. We know that the actual distance is $4.5$ miles and the map - distance is $9$ cm. We set up the proportion $\frac{1}{x}=\frac{9}{4.5}$.
Cross - multiply: $9x = 4.5$.
Solve for $x$: $x=\frac{4.5}{9}=0.5$ miles per cm.

Answer:

1. The two regular pentagons are proportional.
2. The scale is $1$ cm represents $0.5$ miles.