the scale factor of two similar hexagons is 3:4. the perimeter of the smaller hexagon is 60 centimeters. what is the perimeter of the larger hexagon?

To find the perimeter of the larger hexagon, we need to use the scale factor. The scale factor is given as 3:4, which means that every side of the smaller hexagon is multiplied by 3 to get the corresponding side length of the larger hexagon.

Given that the perimeter of the smaller hexagon is 60 centimeters, we can find the length of each side of the smaller hexagon by dividing the perimeter by 6 (since a hexagon has 6 sides).

Perimeter of the smaller hexagon = 60 cm
Length of each side of the smaller hexagon = 60 cm / 6 = 10 cm

Now, to find the length of each side of the larger hexagon, we multiply the length of each side of the smaller hexagon by the scale factor of 3/4.

Length of each side of the larger hexagon = 10 cm * (3/4) = 7.5 cm

Since a hexagon has 6 sides, the perimeter of the larger hexagon is given by:

Perimeter of the larger hexagon = Length of each side of the larger hexagon * 6
Perimeter of the larger hexagon = 7.5 cm * 6 = 45 cm

Therefore, the perimeter of the larger hexagon is 45 centimeters.

To find the perimeter of the larger hexagon, we can use the scale factor.

1. Calculate the scale factor:
The given scale factor is 3:4. To find the actual scale factor, we add the numbers in the ratio:
3 + 4 = 7
Therefore, the actual scale factor is 7.

2. Calculate the ratio of the perimeters:
Since the perimeters of the hexagons are directly proportional to their corresponding sides, we can set up the following equation:
(Perimeter of Smaller Hexagon) : (Perimeter of Larger Hexagon) = (Scale Factor)

Plugging in the given values:
60 : (Perimeter of Larger Hexagon) = 7

3. Solve for the perimeter of the larger hexagon:
To find the perimeter of the larger hexagon, we need to isolate it in the equation. Using algebra, we can rearrange the equation as follows:
(Perimeter of Larger Hexagon) = (Perimeter of Smaller Hexagon) * (Scale Factor)

Plugging in the values:
(Perimeter of Larger Hexagon) = 60 * 7

Calculating:
(Perimeter of Larger Hexagon) = 420 centimeters

Therefore, the perimeter of the larger hexagon is 420 centimeters.

3/4=60/x, cross multiply and solve