the scale factor of two similar polygons as 4:7. the perimeter of the smaller polygon is 320 centimeter what is the perimeter of the larger polygon
since perimeter is a linear measurement ...
P/320 = 7/4
4P = 2240
P = 560
notice 560:320 = 7:4
To find the perimeter of the larger polygon, we need to know the scale factor between the two polygons and the perimeter of the smaller polygon.
Given that the scale factor is 4:7, we can set up the proportion:
4/7 = smaller polygon perimeter / larger polygon perimeter
Since we know that the perimeter of the smaller polygon is 320 centimeters, we can substitute it into the proportion:
4/7 = 320 / larger polygon perimeter
To solve for the larger polygon perimeter, we can cross-multiply and then divide:
4(larger polygon perimeter) = 7 * 320
4(larger polygon perimeter) = 2240
larger polygon perimeter = 2240 / 4
larger polygon perimeter = 560
Therefore, the perimeter of the larger polygon is 560 centimeters.
To find the perimeter of the larger polygon, we need to use the given scale factor and the known perimeter of the smaller polygon.
1. Start by writing down the given information:
- Scale factor: 4:7 (4 to 7 or 4/7)
- Perimeter of the smaller polygon: 320 centimeters
2. Let's assume that the perimeter of the larger polygon is represented by "x". Now we can set up a proportion using the scale factor:
(perimeter of smaller polygon) / (scale factor) = (perimeter of larger polygon) / (scale factor)
Substituting the values we know:
320 / (4/7) = x / 1
3. Simplify the equation by multiplying both sides by the scale factor (4/7):
320 * (7/4) = x
4. Calculate the value of "x":
560 = x
5. Therefore, the perimeter of the larger polygon is 560 centimeters.