Question

In the diagram below, what is the equation that represents the relationship between the number of triangles and the perimeter of the figure they form? Use this table to help you create an equation.

Answer 1

Answer:

The perimeter of the figure as a function of the number of triangles is $y = 6 + 4\cdot x$.

Step-by-step explanation:

According to the diagram, we get the following facts:

i) For one triangle ($x=1$), the total perimeter is ($y=2\cdot 3 + 1\cdot 4 = 10$).

ii) For two triangles ($x = 2$), the total perimeter is ($y = 2\cdot 3 +2\cdot 4 = 14$)

iii) For three triangles ($x = 3$), the total perimeter is ($y = 2\cdot 3 +3\cdot 4 = 18$)

iv) For four triangles ($x = 4$), the total perimeter is ($y = 2\cdot 3 +4\cdot 4 = 22$)

From these information we conclude that the equation that determines the perimeter of the figure as a function of the number of triangles is $y = 6 + 4\cdot x$.