# Perimeter of a triangle

The perimeter of a triangle is the distance around it, which is the sum of the lengths of its sides. The formula for the perimeter of a triangle is:

Perimeter = a + b + c

where a, b, and c are the lengths of the three sides of the triangle.

## Special triangles

Isosceles triangles, equilateral triangles, and right triangles have a number of relationships that allow us to find their perimeters without necessarily knowing all of their side lengths. Below are the formulas for the perimeters of these triangle types.

### Isosceles triangle

Perimeter = 2 × l + b

Where l is the side length and b is the base length.

### Equilateral triangle

Perimeter = 3 × s

Where s is the side length

### Right triangle

You can use the Pythagorean Theorem to find the perimeter of a right triangle if you know, or can determine, the lengths of at least two sides from the given information.

Referencing the triangle above:

If a and b are given,

If a and c are given,

If b and c are given,

Example:

What is the perimeter of a triangle with a hypotenuse c = 26, and a side length a = 10?

Perimeter = | |

= | |

= | 10 + 26 + 24 |

= | 60 |