Question

the figures below are similar. the perimeter of each figure is given.
p₁ = 54 ft p₂ = 42 ft
what is the ratio of the side length of the larger hexagon to the side length 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 polygons, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.

Step2: Calculate the ratio

Let \(P_1 = 54\) (perimeter of the larger hexagon) and \(P_2=42\) (perimeter of the smaller hexagon). The ratio of the perimeters (and thus the ratio of the side lengths) is \(\frac{P_1}{P_2}=\frac{54}{42}\).
Simplify \(\frac{54}{42}\) by dividing both numerator and denominator by \(6\). \(\frac{54\div6}{42\div6}=\frac{9}{7}\).

Answer:

\(9:7\)