Calculate the first few perimeters and find a pattern.
102 cm
Practice makes perfect
Let's find a pattern that we can use to calculate the perimeter of the figure when 100 triangles are put together. In order to find the pattern, we will calculate the perimeter of the figure consisting of 2, 3, 4, and more triangles.
Calculate The First Few Perimeters
Let's start with one triangle. It has three sides each with lengths of 1 cm. The perimeter is the sum of these values.
P_1=1+1+1=3 cm
Notice, the index of P represents the number of triangles connected. Now, let's consider the figure of two triangles put together.
As we can see, there are 4 sides in the figure, each 1 cm in length. Adding these sides, we get the perimeter of the figure.
P_2=1+1+1+1=4 cm
Let's now calculate the perimeter of the figure in which 3 triangles are put together.
The figure contains 5 sides of the triangles, therefore its perimeter is 5 cm.
P_3=5 cm
Find A Pattern
Now let's make a table that shows the information we gathered.
Number of Triangles
Perimeter, cm
1
3
2
4
3
5
As we can see, when adding one more triangle, the perimeter of the figure increased by 1. Also, the perimeter is always greater than the number of triangles in it by 2. We can use this to create a formula.
P_n=n+2
Calculate The Perimeter Of 100 Triangles
We want to calculate the perimeter when 100 triangles are put together. Therefore, we can substitute 100 for n into the formula to calculate P_n.
P_(100)= 100+2=102 cm
The perimeter is 102 cm.
