How do you find the perimeter of a second polygon given just the scale factor of both polygons and the perimeter of the larger polygon?
The problem is
Two similar polygons have a scale factor of 3:5. The perimeter of the large polygon is 120 feet. Find the perimeter of the small polygon.
do not just tell me the answer, but please tell me how you got it as well. Thank you :)
Assume the scale factor is s where s<1 since the second polygon is smaller.
If the scale factor s>1, that means the reciprocal should be use.
Let P=perimeter of the larger polygon, then the perimeter of the smaller polygon is
p=P*s
Did you get 200 for this particular problem? cause that's what I got, which doesn't make sense to me because it's suppose to be less than 120 since it's the smaller polygon
Polygon R and polygon S are similar. The perimeter of polygon R is 192 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 3 cm, what is the length of the corresponding side in polygon R?
16
To find the perimeter of the smaller polygon, given just the scale factor and the perimeter of the larger polygon, you can follow these steps:
1. Understand the concept of a scale factor: The scale factor is the ratio of corresponding side lengths of two similar polygons. In this case, the scale factor is 3:5, which means that every side length of the smaller polygon is 3/5 of the corresponding side length of the larger polygon.
2. Determine the scale factor between the perimeters: Since the scale factor applies to all side lengths, it also applies to the perimeter. Thus, the scale factor between the perimeters of the two polygons is also 3:5.
3. Set up a proportion: Let 'x' represent the perimeter of the smaller polygon. Then, you can set up the proportion:
(perimeter of smaller polygon) / (perimeter of larger polygon) = (scale factor of smaller polygon) / (scale factor of larger polygon)
x / 120 = 3 / 5
4. Solve the proportion: Cross-multiply and solve for 'x':
5x = 3 * 120
5x = 360
x = 360 / 5
x = 72
Therefore, the perimeter of the smaller polygon is 72 feet.