Final answer:
The ratio of the perimeters of the hexagons is 3:4.
Step-by-step explanation:
To find the ratio of the perimeters of the hexagons, we first need to find the side length of the larger hexagon. The given ratio of the side lengths is 3:4. Let's set up a proportion:
1½ / x = 3 / 4
Cross multiply and solve for x:
4 * 1½ = 3 * x
6 = 3x
x = 2 inches
So the side length of the larger hexagon is 2 inches. Now we can find the ratios of the perimeters:
Perimeter of smaller hexagon = 6 * 1½ = 9 inches
Perimeter of larger hexagon = 6 * 2 = 12 inches
The ratio of the perimeters is 9:12, which simplifies to 3:4.