# 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.

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