What is a Scalene Triangle? (Definition & Examples) - BYJUS

# Scalene Triangle

In geometry, a triangle is defined as a three-sided closed plane shape with three vertices and three angles. There are various types of triangle but in the following article we will learn about scalene triangles and will understand their properties by some real life examples. ...Read MoreRead Less

## What is a Scalene Triangle?

A triangle in which all three sides are of different lengths and all the three angles of the triangle are also of different measures, is called a scalene triangle.

In comparison an isosceles triangle has two equal sides and an equilateral triangle has three equal sides.

A scalene triangle with three vertices, A, B, and C, is represented as $$\triangle ABC$$

Therefore, it is clear from this image of a scalene triangle that, AB ≠ BC ≠ CA.

## Real-Life Examples of Scalene Triangles

The most common examples of scalene triangles in our daily lives are sailboats, ramps, and roof trusses.

## Properties of Scalene Triangle

1. All the sides of the scalene triangle are unequal.
2. All the angles of the scalene triangle are unequal.
3. As it has no equal sides, hence there is no line of symmetry.
4. It has no point of symmetry.
5. A scalene triangle can be an acute angle, an obtuse angle or a right angle triangle.
6. The formula for the area of a scalene triangle is:

A = $$\sqrt{s~\times~(s-a)~\times~(s-b)~\times~(s-c)}$$

Where, $$s=\frac{a~+~b~+~c}{2}$$

## Solved Scalene Triangle Examples

Example 1: Classify the triangle based on its sides.

Solution:

From the figure, sides of the triangle are 7 cm, 15 cm and 12 cm.

All the sides of the triangle are unequal in length that is

7 ≠ 12 ≠ 15

Hence, it is a scalene triangle.

Example 2: Classify the triangular park according to its sides and then determine the park’s perimeter.

Solution:

From the figure-

Sides of the triangular park are 40 m, 60 m and 90 m

So, all sides of the triangular park are not in the same length.

As a result, it’s a scalene triangle.

To determine its perimeter, find the sum of all the side lengths of the park.

90 + 60 + 40 = 190

Hence, the perimeter of the triangular park is 190  meters.

Example 3: Classify the triangle based on its angles.

Solution:

From the figure, angles of the triangle are 36 degrees, 54 degrees  and 90 degrees.

All the angles of the triangle are not the same.

Hence, it is a scalene triangle.

A triangle with all of its sides are unequal in length is known as a scalene triangle.

As it has no equal sides, there is no line of symmetry in a scalene triangle.

In an equilateral triangle all the three sides are equal in length. However, in a scalene triangle all the three sides are not equal in length.

Based on its sides, a triangle is classified as follows:

1. Equilateral triangle
2. Isosceles triangle
3. Scalene triangle

The perimeter of a scalene triangle is equal to the sum of all of its sides.