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.

Calculate The First Few Perimeters

Find A Pattern

Calculate The Perimeter Of 100 Triangles

Calculate The Perimeter Of $100$ Triangles

{{ 'ml-heading-exercise' | message }} {{ exercise.name }} {{ 'ml-label-page' | message }} {{ exercise.page }}