two similiar hexagons have a scale factor of 5:2 the perimeter of the larger hexagon is 45cm. Whats the perimeter of the smaller hexagon?
18cm
Well, if the larger hexagon has a perimeter of 45cm and the scale factor is 5:2, we can do some mathematical clownery to find the perimeter of the smaller hexagon.
Let's set up a ratio:
5 (the scale factor of the larger hexagon) : 2 (the scale factor of the smaller hexagon) = Perimeter of the larger hexagon : Perimeter of the smaller hexagon
So, we have 5:2 = 45:x, where x is the perimeter of the smaller hexagon.
To find x, we can use some clowndivision (division):
5/2 = 45/x
Cross multiplying, we get:
5x = 90
Dividing both sides by 5, we find the value of x:
x = 18
So, the perimeter of the smaller hexagon is 18cm.
To find the perimeter of the smaller hexagon, we need to apply the scale factor of 5:2 to the perimeter of the larger hexagon.
Let's assume the perimeter of the smaller hexagon is P.
The scale factor of 5:2 means that every length in the larger hexagon is 5 times the corresponding length in the smaller hexagon.
Therefore, if the perimeter of the larger hexagon is 45 cm, then each side length of the larger hexagon is 45/6 = 7.5 cm.
Since the scale factor is 5:2, each side length of the smaller hexagon is 7.5/5 = 1.5 cm.
Now, a hexagon has 6 sides, so the perimeter of the smaller hexagon is 6 * 1.5 = 9 cm.
Therefore, the perimeter of the smaller hexagon is 9 cm.
To find the perimeter of the smaller hexagon, let's first understand what a scale factor means in this context.
A scale factor is a ratio that represents the proportional relationship between corresponding sides of two similar figures. In this case, the scale factor of 5:2 means that every side length of the larger hexagon is five times the length of the corresponding side of the smaller hexagon.
Since the perimeter is simply the sum of all the side lengths of a polygon, we can determine the perimeter of the smaller hexagon using the scale factor and the known perimeter of the larger hexagon.
1. Start by finding the length of one side of the larger hexagon. Divide the perimeter of the larger hexagon by the number of sides (6 in this case).
Length of one side of the larger hexagon = Perimeter / Number of sides
Length of one side of the larger hexagon = 45 cm / 6 = 7.5 cm
2. Now, we can use the scale factor to find the length of one side of the smaller hexagon.
Length of one side of the smaller hexagon = Length of one side of the larger hexagon / Scale factor
Length of one side of the smaller hexagon = 7.5 cm / (5/2) = 7.5 cm * (2/5) = 3 cm
3. Finally, calculate the perimeter of the smaller hexagon by multiplying the length of one side by the number of sides.
Perimeter of the smaller hexagon = Length of one side of the smaller hexagon * Number of sides
Perimeter of the smaller hexagon = 3 cm * 6 = 18 cm
Therefore, the perimeter of the smaller hexagon is 18 cm.
45 * 2/5
ALL lengths proportion by the scale factor
all areas by the factor squared
all volumes by the factor cubed