# In the pentagon ABCDE AB = BC = CD = DE = AE = 8 cm. How will the perimeter of this pentagon change

**In the pentagon ABCDE AB = BC = CD = DE = AE = 8 cm. How will the perimeter of this pentagon change if: a) all its sides are increased 5 times; b) reduce its sides by a factor of 5? What is the ratio of the perimeter of pentagon ABCDE to its side?**

The perimeter of any polygon, pentagon in particular, is equal to the sum of the values of all its sides.

1) Hence, the perimeter P (ABCDE) = AB + BC + CD + DE + AE = 8 (cm) * 5 = 40 (cm).

a) When each side is enlarged 5 times, the perimeter will also increase 5 times. Let’s prove it:

P 5 (ABCDE) = 5 * AB + 5 * BC + 5 * CD + 5 * DE + 5 * AE =

5 * (AB + BC + CD + DE + AE) = 5 * P (ABCDE) = 5 * 40 = 200 (cm).

That is, the perimeter has increased 5 times, like each side.

b) P (1/5 ABCDE) = 1/5 P (ABCDE) = 40/5 = 8 (cm).

P (ABCDE) / AB = 40/8 = 5. P (5ABCDE) / (AB * 5) = 200/5 * 8 = 5.