Question

find the relationship between the number of shapes and the perimeter of the figure they form Write an equation to represent this relationship?
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Answer 1

Answer:

p = 3n + 2

Step-by-step explanation:

let n be the number of shapes and p the perimeter

We can construct the following table

n : 1    2    3

p : 5   8    11

The differences in p are constant

8 - 5 = 11 - 8 = 3

Thus p = 3n + ?

n = 1 → 3(1) + ? = 5 ⇒ 3 + ? = 5 ⇒ ? = 2

n = 2 → 3(2) + ? = 8 ⇒ 6 + ? = 8 ⇒ ? = 2

n = 3 → 3(3) + ? = 11 ⇒ 9 + ? = 11 ⇒ ? = 2

We require to add 2 to 3n

Thus

p = 3n + 2