Question

the figures below are similar. the labeled sides are corresponding.
what is the ratio of the perimeter of the larger hexagon to the perimeter of the smaller hexagon?
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: Calculate the ratio of the corresponding side lengths

The length of the corresponding side of the larger hexagon is \(8\) mm and that of the smaller hexagon is \(6\) mm. The ratio of the side lengths is \(\frac{8}{6}\).

Step3: Simplify the ratio

\(\frac{8}{6}=\frac{4}{3}\) (dividing numerator and denominator by \(2\)).

Answer:

\(4:3\)