# Perimeter of Triangle – Formula with Examples

Welcome to Brighterly, where our mission is to make math exciting and enjoyable for children of all ages! Today, we’re exploring the fascinating world of geometry, focusing on the perimeter of a triangle. This fundamental concept is essential for students to grasp as it sets the foundation for more advanced mathematical topics. So, without further ado, let’s embark on an adventure into the realm of triangle perimeters and discover the secrets behind this geometric wonder!

## What is the Perimeter of a Triangle?

The perimeter of any shape refers to the total length of its outer edges. In the case of a triangle, the perimeter is the sum of the lengths of its three sides. Triangles come in various types, including scalene, isosceles, equilateral, and right triangles. Depending on the type of triangle, the method of calculating its perimeter may vary slightly. Keep reading to learn how to find the perimeter of a triangle and the formulas for each type of triangle!

## How to Find The Perimeter of a Triangle?

Finding the perimeter of a triangle is quite simple! All you need to do is add up the lengths of its three sides. However, if you’re missing some side lengths, you may need to use other information about the triangle to find the missing values. For instance, you could use the Pythagorean theorem for right triangles or apply the properties of isosceles and equilateral triangles. Below, we’ll discuss the formulas for finding the perimeter of various triangle types.

## Perimeter of a Triangle Formula

The general formula for finding the perimeter of a triangle is:

`Perimeter = a + b + c`

where ‘a’, ‘b’, and ‘c’ represent the lengths of the triangle’s sides.

This formula applies to all types of triangles, but some specific triangle types have unique properties that can simplify the calculation. Let’s explore the formulas for each triangle type!

## Perimeter of a Scalene Triangle

A scalene triangle has three sides of different lengths. To find the perimeter of a scalene triangle, simply use the general formula:

`Perimeter = a + b + c`

## Perimeter of an Isosceles Triangle

An isosceles triangle has two sides of equal length. Since two sides are equal, the formula for its perimeter is:

`Perimeter = 2a + b`

where ‘a’ is the length of the equal sides and ‘b’ is the length of the remaining side.

## Perimeter of an Equilateral Triangle

An equilateral triangle has three sides of equal length. Therefore, the formula for its perimeter is:

`Perimeter = 3a`

where ‘a’ is the length of each side.

## Perimeter of a Right Triangle

A right triangle has one 90-degree angle. To find its perimeter, you can use the general formula:

`Perimeter = a + b + c`

However, if you only have the lengths of the two legs (the sides adjacent to the right angle), you can use the Pythagorean theorem to find the length of the hypotenuse (the side opposite the right angle):

`c² = a² + b²`

Then, you can calculate the perimeter using the general formula.

## Perimeter of Isosceles Right Triangle

An isosceles right triangle has one 90-degree angle and two equal sides. Since the equal sides are adjacent to the right angle, you can use the Pythagorean theorem to find the hypotenuse:

`c² = a² + a²`

Then, calculate the perimeter using the general formula.

## Perimeter of an Isosceles, Equilateral and Scalene Triangle

As a recap, here are the formulas for finding the perimeter of isosceles, equilateral, and scalene triangles:

• Isosceles: `Perimeter = 2a + b`
• Equilateral: `Perimeter = 3a`
• Scalene: `Perimeter = a + b + c`

Keep these formulas in mind as we explore some examples below!

## Perimeter of a Triangle Examples

Let’s take a look at some examples to help you understand how to find the perimeter of a triangle:

1. Scalene Triangle: If a scalene triangle has sides with lengths of 5, 7, and 8, the perimeter is: `Perimeter = 5 + 7 + 8 = 20`

2. Isosceles Triangle: If an isosceles triangle has two equal sides with lengths of 6 and a remaining side with a length of 4, the perimeter is: `Perimeter = 2(6) + 4 = 12 + 4 = 16`

3. Equilateral Triangle: If an equilateral triangle has sides with lengths of 9, the perimeter is: `Perimeter = 3(9) = 27`

## Practice Questions on Perimeter of Triangle

1. A scalene triangle has sides with lengths of 6, 10, and 8. What is its perimeter?
2. An isosceles triangle has two equal sides with lengths of 5 and a remaining side with a length of 2. What is its perimeter?
3. An equilateral triangle has sides with lengths of 7. What is its perimeter?

## Conclusion

We hope this comprehensive guide on the perimeter of a triangle has not only helped you grasp the concept but also inspired a newfound appreciation for geometry. At Brighterly, we believe that practice is the key to unlocking your full potential. So, don’t hesitate to tackle more problems and apply the formulas for each triangle type. As you continue to hone your skills, you’ll soon become a master at calculating triangle perimeters and be ready to tackle even more complex mathematical challenges!

Remember, learning should be a joyous journey, and at Brighterly, we’re dedicated to making that journey as enjoyable and engaging as possible. Keep exploring, stay curious, and most importantly, have fun!

## Frequently Asked Questions on Perimeter of Triangle

### What is the perimeter of a triangle?

The perimeter of a triangle is the total length of its outer edges or the sum of the lengths of its three sides. Perimeter is an important concept in geometry and is used to measure the boundary of any shape. In the case of triangles, the perimeter helps us understand the size and scale of the triangle based on the lengths of its sides.

### How do you find the perimeter of a triangle?

To find the perimeter of a triangle, you need to add the lengths of its three sides. The method of calculating the perimeter may vary slightly depending on the type of triangle (scalene, isosceles, equilateral, or right triangle). For each triangle type, there is a specific formula that can be used to calculate the perimeter:

• Scalene: `Perimeter = a + b + c`
• Isosceles: `Perimeter = 2a + b`
• Equilateral: `Perimeter = 3a`
• Right Triangle: `Perimeter = a + b + c` (use the Pythagorean theorem if necessary)

### What is the formula for the perimeter of a triangle?

The general formula for the perimeter of a triangle is `Perimeter = a + b + c`, where ‘a’, ‘b’, and ‘c’ represent the lengths of the triangle’s sides. This formula applies to all types of triangles, but some specific triangle types have unique properties that can simplify the calculation. For example, an isosceles triangle has two equal sides, so its formula is `Perimeter = 2a + b`, and an equilateral triangle has three equal sides, so its formula is `Perimeter = 3a`.

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