Question

the figures below are similar. the labeled sides are corresponding.

$p_1 = ?$
$p_2 = 36$ in

what is the perimeter of the smaller hexagon?
$p_1 = \square$ inches

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides is $\frac{3}{6}=\frac{1}{2}$.

Step2: Use the scale factor for perimeters

Since the ratio of perimeters of similar figures is equal to the ratio of their corresponding sides, let $P_1$ be the perimeter of the smaller hexagon. We have $\frac{P_1}{P_2}=\frac{1}{2}$. Substituting $P_2 = 36$ in, we get $P_1=\frac{1}{2}\times36$.

Step3: Calculate $P_1$

$\frac{1}{2}\times36 = 18$.

Answer:

18