Question

the figures below are similar. the perimeter of each figure is given.

p₁ = 42 in p₂ = 12 in

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 figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Let the ratio of the side length of the larger hexagon to the side length of the smaller hexagon be \(a:b\). Then, if \(P_1\) is the perimeter of the larger hexagon and \(P_2\) is the perimeter of the smaller hexagon, we have \(\frac{a}{b}=\frac{P_1}{P_2}\).

Step2: Substitute the given perimeters

We are given \(P_1 = 42\) in and \(P_2=12\) in. So, \(\frac{P_1}{P_2}=\frac{42}{12}\).

Step3: Simplify the fraction

Simplify \(\frac{42}{12}\) by dividing both the numerator and the denominator by their greatest - common divisor. The GCD of 42 and 12 is 6. \(\frac{42\div6}{12\div6}=\frac{7}{2}\)

Answer:

\(7:2\)