Question

the figures below are similar. the labeled sides are corresponding.
4.6 mm
0.7 mm
p₁ = 4.2 mm
p₂= ?
what is the perimeter of the larger hexagon?
p₂ = millimeters

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides of similar figures is the scale factor. Let the side of the smaller hexagon be \( s_1 = 0.7 \) mm and the side of the larger hexagon be \( s_2 = 4.6 \) mm. The scale factor \( k=\frac{s_2}{s_1}=\frac{4.6}{0.7}\).

Step2: Use the scale factor for perimeters

For similar figures, the ratio of perimeters is equal to the scale factor. Let \( P_1 = 4.2 \) mm (perimeter of smaller hexagon) and \( P_2 \) be the perimeter of the larger hexagon. So, \(\frac{P_2}{P_1}=k\), which means \( P_2 = P_1\times\frac{s_2}{s_1} \). Substitute the values: \( P_2 = 4.2\times\frac{4.6}{0.7} \). First, calculate \( \frac{4.2}{0.7}=6 \), then \( 6\times4.6 = 27.6 \).

Answer:

\( 27.6 \)