Question

the figures below are similar. the labeled sides are corresponding.
what is the ratio of the perimeter of the smaller hexagon to the perimeter of the larger hexagon?
write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Recall perimeter of regular hexagon

A regular hexagon has 6 equal sides. Let the side length of the smaller hexagon be \( s_1 = 1\space m \) and the side length of the larger hexagon be \( s_2 = 2\space m \). The perimeter \( P \) of a regular hexagon is \( P = 6\times \text{side length} \).

Step2: Calculate perimeters

Perimeter of smaller hexagon, \( P_1 = 6\times s_1 = 6\times1 = 6\space m \).
Perimeter of larger hexagon, \( P_2 = 6\times s_2 = 6\times2 = 12\space m \).

Step3: Find the ratio

The ratio of the perimeter of the smaller hexagon to the larger one is \( \frac{P_1}{P_2}=\frac{6}{12}=\frac{1}{2} \), which as a ratio is \( 1:2 \).

Answer:

\( 1:2 \)