Question

the figures below are similar. the labeled sides are corresponding.
9 m
6 m
p₁ = 54 m
p₂ = ?
what is the perimeter of the smaller hexagon?
p₂ = meters

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides is $\frac{6}{9}=\frac{2}{3}$.

Step2: Use the scale factor for perimeters

Since the perimeters of similar figures are in the same ratio as their corresponding sides, we have $\frac{P_2}{P_1}=\frac{2}{3}$. Given $P_1 = 54$ m, we solve for $P_2$: $P_2=\frac{2}{3}\times54$.

Step3: Calculate $P_2$

$\frac{2}{3}\times54 = 36$.

Answer:

36