Question

the figures below are similar. the labeled sides are corresponding.

what is the ratio of the perimeter of the larger pentagon to the perimeter of the smaller pentagon?

write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Recall the property of similar figures

For similar figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.

Step2: Identify the corresponding side lengths

The side length of the larger pentagon is \( 6 \) ft and the side length of the smaller pentagon is \( 3 \) ft.

Step3: Calculate the ratio of perimeters

The ratio of the perimeter of the larger pentagon to the smaller one is the same as the ratio of their corresponding sides, so it is \( \frac{6}{3}=\frac{2}{1} \), which can be written as \( 2:1 \).

Answer:

\( 2:1 \)