Scalene Triangle
In geometry, a scalene triangle, as the name says is a triangle that has all unequal sides. Since all the three sides are unequal, this means all the three angles are also of different measures. It is one of the three types of triangles based on the properties of its sides. hence when none of the sides of a triangle are equal, we call it a scalene triangle.
What is a Scalene Triangle?
A scalene triangle is a triangle having all three sides of different lengths, and all three angles of different measurements. However, the different measurements don't affect the sum of all the interior angles of the scalene triangle. The sum of the three interior angles always add up to 180 degrees, which satisfies the angle sum property of the triangle.
In the above triangle, you can observe that all 3 symbols on each side are different which denotes that all 3 sides are unequal.
Properties of Scalene Triangle
A scalene triangle is a type of triangle with all its three sides having different lengths with the sum of three of its angles being equal to 180 degrees. It has a wide range of properties. Some of the important properties of a scalene triangle are given below.
 It has three sides, each of a different length.
 It has three angles, each of different measurements.
 It has no parallel or equal sides and hence no line of symmetry.
 There is no point symmetry.
 The interior angles of the triangle can be acute, obtuse, or right angles. Thus, a scalene triangle can be an obtuseangled, acuteangled, or rightangled triangle.
 In the case of an acute scalene triangle, the center of the circumscribing circle will lie inside the triangle.
 In an obtuse scalene triangle, the circumcenter will lie outside the triangle.
Difference Between Equilateral, Isosceles, and Scalene Triangles
Triangles are classified into three types  equilateral, isosceles, and scalene triangle based on the sides. The main points of difference between these three types of triangles are as discussed below:
Equilateral Triangle  Isosceles Triangle  Scalene Triangle 
When all the three sides of the triangles are equal in length, it is an equilateral triangle.  When any two sides of the triangle are equal in length, it is an isosceles triangle.  When all the three sides of the triangle are of different measures, it is a scalene triangle. 
All three angles are of equal measure. Each measures 60 degrees.  Angles opposite to equal sides are equal(Isosceles Triangle Theorem)  All three angles of the triangle are of different measurements. 
Scalene Triangle Formula
The two main scalene triangle formulas include  the perimeter of the scalene triangle and the area of the scalene triangle.
Perimeter of a scalene triangle
The perimeter of a triangle = sum of all the three sides of the triangle = (a + b + c) units. Thus, the perimeter of the scalene triangle = (a + b + c) units, where a, b, and c denote all three sides of the scalene triangle.
Area of a scalene triangle
The area of a triangle =(1/2) x b x h square units. Here,
 “b” refers to the base of the triangle
 “h” refers to the height of the triangle
But if the height and base are not given, but sides of the triangle are known, then apply Heron’s formula. Thus, Area of the scalene triangle, \(\begin{equation} A=\sqrt{s(sa)(sb)(sc)}\end{equation}\) square units. Here, s is the semi perimeter of a triangle which is, s = (a+b+c)/2, and a, b, and c denotes the sides of the triangle.
Important Notes
 A scalene triangle has three sides, each of a different length and three angles each of different measurements.
 It also follows the angle sum property of the triangle.
 Since the lengths of sides are unequal and even angles are of different measures, a scalene triangle doesn't show symmetry.
Scalene Triangle Related Topics
Check out these interesting articles related to the scalene triangle and its related topics.
 Area of Scalene Triangle
 Acute Triangle
 Rightangled Triangle
 Obtuse Triangles
 Isosceles Triangles
 Isosceles Triangles Formula
 Equilateral Triangle Formulas
 Area of Triangle
 Area of an Equilateral Triangle
 Area of Similar Triangles
 Similar Triangles Formula
Solved Examples on Scalene Triangle

Example 1: If the sides of a triangle are given to be 9 cm, 13 cm, and 14 cm. Can we say that it's a scalene triangle?
Solution:
All three sides of the triangle are of different measures, 9cm, 13cm, and 14cm. Therefore, we can say that it is a scalene triangle.

Example 2: Calculate the perimeter of the triangle with sides 28 units, 39 units, and 18 units.
Solution:
The sides of the triangle are given as 28 units, 39 units, and 18 units. Therefore, the perimeter of the triangle = sum of the sides = (28 + 39 + 18) units = 85 units.

Example 3: The length of the sides of a triangle ABC are 4 units, 3 units, and 5 units. Calculate its area.
Solution:
Let a = 4 units, b = 3 units, c = units . Using Heron's Formula: Area of triangle = √(s(sa)(sb)(sc) square units. We will first find s, s = (a+b+c)/2 ⇒ s = (4+3+5)/2 ⇒ s = 6. Now, put the values. Thus, A = √(6(64)(63)(65)) = √(6(2)(3)(1)) = √(36) = 6 units^{2}. Therefore, the area of the triangle is 6 units^{2}.
FAQs on Scalene Triangle
What is a Scalene and an Isosceles Triangle?
An isosceles triangle has two out of the three sides that are of the same length whereas a scalene triangle has none of the sides of the same length.
What are the Lengths of a Scalene Triangle?
Scalene triangles are triangles with sides of different lengths or simply a triangle with noncongruent sides. For example, a triangle of side lengths of 2 cm, 3 cm, and 4 cm can be considered a scalene triangle.
How do you Classify a Scalene Triangle?
A scalene triangle can be classified as an acuteangled triangle, an obtuseangled triangle, and a rightangled triangle:
 In the case of an acute scalene triangle, the center of the circumscribing circle will lie inside the triangle.
 In an obtuse scalene triangle, the circumcenter will lie outside the triangle.
 In the case of a rightangled triangle, the circumcenter is at the midpoint of the hypotenuse.
What is the Formula for Area of Scalene triangle?
The area of a scalene triangle can be calculated using the formula: √s(s−a)(s−b)(s−c) or when the base and height of the triangle are given, then we apply the following formula: (1/2) × b × h.
Can Scalene Triangles be Congruent?
A triangle with no congruent sides or angles is called a scalene triangle. Two scalene triangles can be congruent if they follow up any of the congruency rules.
What is the Perimeter of Scalene Triangle?
The perimeter of a scalene triangle can be calculated using the formula: a + b + c (sum of all sides).