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
- All the sides of the scalene triangle are unequal.
- All the angles of the scalene triangle are unequal.
- As it has no equal sides, hence there is no line of symmetry.
- It has no point of symmetry.
- A scalene triangle can be an acute angle, an obtuse angle or a right angle triangle.
- The formula for the area of a scalene triangle is:
A = \(\sqrt{s~\times~(s-a)~\times~(s-b)~\times~(s-c)}\)
Where, \(s=\frac{a~+~b~+~c}{2}\)
Rapid Recall
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:
- Equilateral triangle
- Isosceles triangle
- Scalene triangle
The perimeter of a scalene triangle is equal to the sum of all of its sides.