The perimeter of a scalene triangle is defined by the outer contour of the figure. The perimeter is the total length of the outer contour. We can also look at this differently by considering the perimeter as the total length of the figure. Recall that the scalene triangle is a geometric figure that has three sides and three vertices, in which the lengths of the three sides are different from each other.

Here, we will learn about the formula for the perimeter of a scalene triangle and we will use it to solve some problems.

##### GEOMETRY

**Relevant for**…

Learning about the perimeter of a scalene triangle with examples.

##### GEOMETRY

**Relevant for**…

Learning about the perimeter of a scalene triangle with examples.

## What is the formula to find the perimeter of a scalene triangle?

To find the perimeter of a scalene triangle, we need to know the lengths of all the sides of the triangle. In a scalene triangle, the lengths of the three sides are different, so we can use different letters to represent each side. Therefore, knowing these lengths, the perimeter is the sum of all the lengths:

$latex p=a+b+c$ |

where,

- $latex a=$ length of base
- $latex b=$ length of lateral side
- $latex c=$ length of opposite side

## Perimeter of a scalene triangle – Examples with answers

The perimeter formula is used to solve the following examples. Each example has its respective solution, in which you can look at the process and reasoning used. Try to solve the exercises yourself before looking at the answer.

**EXAMPLE 1**

What is the perimeter of a scalene triangle that has sides of lengths 6 m, 7 m, and 8 m?

##### Solution

We have the following lengths:

- Side 1, $latex a=6$ m
- Side 2, $latex b=7$ m
- Side 3, $latex c=8$ m

We can use the perimeter formula with these values:

$latex p=a+b+c$

$latex p=6+7+8$

$latex p=21$

The perimeter of the triangle is 21 m.

**EXAMPLE 2**

What is the perimeter of a scalene triangle with side lengths 11 m, 13 m, and 14 m?

##### Solution

We have the following sides:

- Side 1, $latex a=11$ m
- Side 2, $latex b=13$ m
- Side 3, $latex c=14$ m

We use these values with the perimeter formula:

$latex p=a+b+c$

$latex p=11+13+14$

$latex p=38$

The perimeter of the triangle is 38 m.

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**EXAMPLE 3**

A scalene triangle has sides of lengths 23 cm, 25 cm, and 31 cm. What is its perimeter?

##### Solution

We can identify the following:

- Side 1, $latex a=23$ cm
- Side 2, $latex b=25$ cm
- Side 3, $latex c=31$ cm

Therefore, we use these values in the formula:

$latex p=a+b+c$

$latex p=23+25+31$

$latex p=79$

The perimeter of the triangle is 79 cm.

**EXAMPLE 4**

A scalene triangle has a perimeter of 86 m and sides of length 32 m and 28 m. What is the length of the third side?

##### Solution

We can observe the following information:

- Perimeter, $latex p=86$ m
- Side 1, $latex a=32$ m
- Side 2, $latex b=28$ m

We use these values in the perimeter formula and solve for *c*:

$latex p=a+b+c$

$latex 86=32+28+c$

$latex 86=60+c$

$latex c=26$

The third side has a length of 26 m.

**EXAMPLE 5**

If a scalene triangle has a perimeter of 59 cm and sides of lengths 17 cm and 19 cm, what is the length of the third side?

##### Solution

We have the following information:

- Perimeter, $latex p=59$ cm
- Side 1, $latex a=17$ cm
- Side 2, $latex b=19$ cm

We solve for *c*:

$latex p=a+b+c$

$latex 59=17+19+c$

$latex 59=36+c$

$latex c=23$

The length of the third side is 23 cm.

## Perimeter of a scalene triangle – Practice problems

Solve the following problems using the formula for the perimeter of scalene triangles. Select an answer and click “Check” to check that you got the correct answer.

## See also

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

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