The perimeter of an isosceles triangle is the total contour around the triangle. This means that the perimeter is calculated by adding the lengths of all the sides of the triangle. In an isosceles triangle, we have two sides that have the same length. Therefore, the perimeter formula is simplified by combining the congruent side lengths.

Here, we will learn about the formula for the perimeter of an isosceles triangle. In addition, we will use this formula to solve some problems.

##### GEOMETRY

**Relevant for**…

Learning about the perimeter of an isosceles triangle with examples.

##### GEOMETRY

**Relevant for**…

Learning about the perimeter of an isosceles triangle with examples.

## Formula for the perimeter of an isosceles triangle

The perimeter of any triangle can be calculated by adding the lengths of all the sides of the triangle. Therefore, we have the formula:

$latex p=a+b+c$

where, $latex a, ~b, ~c$ are the lengths of the sides of the triangle.

Since an isosceles triangle has two sides of equal length, we can calculate its perimeter using the formula:

$latex p=b+2a$ |

where *b* is the length of the base and *a* is the length of the congruent sides.

## Perimeter of an isosceles triangle – Examples with answers

The formula for the perimeter of isosceles triangles is used to solve the following examples. Try to solve the exercises yourself before looking at the answer.

**EXAMPLE 1**

What is the perimeter of an isosceles triangle that has a base of length 11 m and congruent sides of length 8 m?

##### Solution

We have the following values:

- Base, $latex b=11$ m
- Sides, $latex a=8$ m

Using the perimeter formula, we have:

$latex p=b+2a$

$latex p=11+2(8)$

$latex p=11+16$

$latex p=27$

The perimeter of the triangle is 27 m.

**EXAMPLE 2**

An isosceles triangle has a base of 12 m and congruent sides of length 15 m. What is its perimeter?

##### Solution

From the question, we have the following information:

- Base, $latex b=12$ m
- Sides, $latex a=15$ m

Using the perimeter formula, we have:

$latex p=b+2a$

$latex p=12+2(15)$

$latex p=12+30$

$latex p=42$

The perimeter of the triangle is 42 m.

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**EXAMPLE 3**

An isosceles triangle has congruent sides of length 22 cm and a base of 15 cm. What is its perimeter?

##### Solution

We can observe the following values:

- Base, $latex b=15$ cm
- Sides, $latex a=22$ cm

Substituting these values in the formula, we have:

$latex p=b+2a$

$latex p=15+2(22)$

$latex p=15+44$

$latex p=59$

The perimeter of the triangle is 59 cm.

**EXAMPLE 4**

If an isosceles triangle has a perimeter of 38 m and congruent sides of 13 m, what is the length of its base?

##### Solution

Here, we start with the perimeter and want to find the length of the base, so we start with the following information:

- Perimeter, $latex p=38$ m
- Sides, $latex a=13$ m

Using the perimeter formula, we have:

$latex p=b+2a$

$latex 38=b+2(13)$

$latex 38=b+26$

$latex b=12$

The length of the base is 12 m.

**EXAMPLE 5**

An isosceles triangle has a base of length 25 m and a perimeter of 55 m. What is the length of one of the congruent sides of the triangle?

##### Solution

We have the following values:

- Perimeter, $latex p=55$ m
- Base, $latex b=25$ m

We use the perimeter formula and solve for *a*:

$latex p=b+2a$

$latex 55=25+2a$

$latex 2a=30$

$latex a=15$

The length of one of the congruent sides of the triangle is 15 m.

## Perimeter of an isosceles triangle – Practice problems

Put into practice the use of the perimeter formula and solve the following problems. Select an answer and click “Check” to verify that you selected the correct answer.

## See also

Interested in learning more about isosceles triangles? Take a look at these pages:

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