Final answer:
The scale factor between the two similar pentagons is determined by the ratio of their perimeters, which is 3:1. Therefore, the scale factor is 3.
Step-by-step explanation:
The student has asked a question about determining the scale factor between two similar pentagons, one with larger sides and the other with smaller side
The larger pentagon has a side length of 4x and a perimeter of 60cm, while the smaller pentagon has a side length of x and a perimeter of 20cm.
To find the scale factor, we can look at the ratio of the perimeters of the two pentagons.
Since the perimeters are in the ratio of 60:20, which simplifies to 3:1, this tells us that the large pentagon is three times as large as the smaller one, meaning the scale factor is 3.