Final answer:
To calculate the outside perimeter of the design made from 10 regular pentagons with a perimeter of 10 cm each, we assume a ring arrangement with 3 sides per pentagon contributing to the outside perimeter, resulting in a total outside perimeter of 60 cm.
Step-by-step explanation:
To find the outside perimeter of the design made from 10 regular pentagons, we first need to determine how many sides of pentagons contribute to the outside perimeter. Since each pentagon has 5 sides and they share sides with each other, not all sides will count towards the outside perimeter.
If the design has all its pentagons arranged in such a way that all of them share sides with each other (such as in a tessellation), then only the outermost sides of the outer pentagons will count towards the outside perimeter.
Let's assume that the design has a ring shape, where each pentagon shares two sides with its neighboring pentagons, and the remaining three sides contribute to the outside perimeter. With 10 pentagons, this would mean we have 10 x 3 sides contributing to the outside perimeter. As the perimeter of each pentagon is 10 cm, each side of a pentagon is 10 cm / 5 = 2 cm.
Therefore, to calculate the outside perimeter of the design, we multiply the number of contributing sides by the length of each side: Outside perimeter = 10 pentagons x 3 sides/pentagon x 2 cm/side = 60 cm.