The scalene triangle is the triangle with all unequal sides. All three sides of the triangle are unequal, so all three angles are also different in length. Based on the properties of its sides, it is one of three types of triangles. A scalene triangle is one in which none of the sides are equal.

## 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. But the sum of all the interior angles of the scalene triangle is unchanged regardless of the different measurements. The sum of the three interior angles always adds up to 180 degrees, which satisfies the angle sum property of the triangle.

There are three symbols on each side of the triangle that are different, which indicates that all three sides are unequal.

## Properties of Scalene Triangle

All three sides of a scalene triangle have different lengths, while the sum of its angles equals 180 degrees. It has a wide range of properties. Below are some of the important properties of a scalene triangle.

- Each of its three sides is different in length.
- In addition, the angles are each measured differently.
- There are no parallel or equal sides, so there is no symmetry.
- There is no point in symmetry.
- Triangles can have acute, obtuse, or right angles as interior angles. Therefore, a scalene triangle can be obtuse-angled, acute-angled, or right-angled.
- A scalene triangle has a circumscribing circle whose center lies inside the triangle.
- The circumcenter of an obtuse scalene triangle lies outside the triangle.

## Scalene Triangle Formula

In addition to the perimeter and area of the scalene triangle, there are two main scalene triangle formulas.

### The 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” indicates the height of the triangle

But if the height and base are not given, but the sides of the triangle are known, then apply Heron’s formula. Thus, the Area of the scalene triangle, A=√s(s−a)(s−b)(s−c)A=s(s−a)(s−b)(s−c) square units. Here, s is the semi perimeter of a triangle which is, s = (a+b+c)/2, and a, b, and c denote 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.
- A triangle’s angle sum property also applies to it.
- Scalene triangles do not show symmetry since the sides have unequal lengths and even angles have different measures.

## Scalene Triangle Examples

**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 scalene 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 scalene 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(s-a)(s-b)(s-c) 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(6-4)(6-3)(6-5)) = √(6(2)(3)(1)) = √(36) = 6 units^{2}. Therefore, the area of the triangle is 6 units^{2}.

## FAQs

**What is Scalene Triangle in Geometry?**

Triangles are two-dimensional shapes with three sides in geometry. This type of triangle has three unequal sides, called the scalene triangle.

**What is a Scalene and an Isosceles Triangle?**

An isosceles triangle has two of its sides of the same length, while a scalene triangle has none of its sides of the same length.

**What are the Lengths of a Scalene Triangle?**

Scalene triangles are triangles with sides of different lengths or simply triangles with sides that are not congruent. A triangle with side lengths of 2 cm, 3 cm, and 4 cm can be considered a scalene triangle.

**How do you Classify a Scalene Triangle?**

Scalene triangles can be classified as acute-angled triangles, obtuse-angled triangles, and right-angled triangles:

A scalene triangle with an acute angle has a circumscribing circle with its center within the triangle.

The circumcenter of an obtuse scalene triangle lies outside the triangle.

The circumcenter of a right-angled triangle is the midpoint of the hypotenuse.

**Can Scalene Triangles be Congruent?**

It’s called a scalene triangle when its sides and angles are not congruent. A pair of scalene triangles can be congruent if they follow any of the congruency rules.

**What is the Perimeter of Scalene Triangle?**

Scalene triangles can be calculated by using the formula: a + b + c (sum of all sides).