The perimeter of an equilateral triangle is the total length covered by the outline of the figure. We can find the perimeter by adding all the lengths of the sides of the triangle. Since the lengths of the sides of an equilateral triangle are equal, we simply need to know the length of one side to find the perimeter.

Here, we will learn about the formula that we can use to calculate the perimeter of equilateral triangles. In addition, we will apply this formula to solve some problems.

##### GEOMETRY

**Relevant for**…

Learning about the perimeter of an equilateral triangle with examples.

##### GEOMETRY

**Relevant for**…

Learning about the perimeter of an equilateral triangle with examples.

## Formula for the perimeter of an equilateral triangle

The perimeter of an equilateral triangle is the measure of the total length of its limits. To find the perimeter, we have to add the lengths of all the sides. Since an equilateral triangle has all the sides of the same length, we only need the length of one side. We can use the following formula:

$latex p=3a$ |

where *a* is the length of one side of the triangle.

## Perimeter of an equilateral triangle – Examples with answers

In the following examples, we use the formula for the perimeter of equilateral triangles to get the answer. Try to solve the exercises yourself and look at the solution to check your answer.

**EXAMPLE 1**

An equilateral triangle has sides of length 5 m. What is the perimeter?

##### Solution

We can use the perimeter formula with the value $latex a=5$. Therefore, we have:

$latex p=3a$

$latex p=3(5)$

$latex p=15$

The perimeter of the triangle is 15 m.

**EXAMPLE 2**

What is the perimeter of an equilateral triangle that has sides of length 8 m?

##### Solution

We plug $latex a=8$ into the perimeter formula:

$latex p=3a$

$latex p=3(8)$

$latex p=24$

The perimeter of the triangle is 24 m.

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**EXAMPLE 3**

If an equilateral triangle has sides of length 15 cm, what is its perimeter?

##### Solution

We use the value $latex a=15$ in the formula:

$latex p=3a$

$latex p=3(15)$

$latex p=45$

The perimeter of the triangle is 45 cm.

**EXAMPLE 4**

An equilateral triangle has a perimeter of 39 m. What is the length of its sides?

##### Solution

In this case, we start with the perimeter and we want to find the length of one of the sides of the triangle. Therefore, we use the perimeter formula and solve for *a*:

$latex p=3a$

$latex 39=3a$

$latex a=13$

The length of the sides of the triangle is 3 m.

**EXAMPLE 5**

What is the length of the sides of an equilateral triangle that has a perimeter of 102 m?

##### Solution

We use the perimeter formula with $latex p=102$ and solve for *a*:

$latex p=3a$

$latex 102=3a$

$latex a=34$

The length of one side of the triangle is 34 m.

## Perimeter of an equilateral triangle – Practice problems

Practice using the formula for the perimeter of equilateral triangles to solve the following problems. Check out the solved exercises above in case you need help.

See also

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