Question

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

(image of two similar hexagons, blue smaller with side 2 mm, pink larger with side 4 mm. p₁ =? for smaller, p₂ = 24 mm for larger)

what is the perimeter of the smaller hexagon?

p₁ = \boxed{} millimeters

Explanation:

Step1: Find similarity ratio

$\text{Ratio} = \frac{\text{Small side}}{\text{Large side}} = \frac{2}{4} = \frac{1}{2}$

Step2: Relate perimeters via ratio

Since perimeters of similar figures are proportional to the ratio of corresponding sides:
$P_1 = P_2 \times \text{Ratio}$
$P_1 = 24 \times \frac{1}{2}$

Answer:

12 millimeters