Mathematics# Scalene triangle

## What is the scalene triangle?

## Characteristics of the scalene triangle

## Properties

## Elements

## Height

## Area

## Perimeter

## Angles

## Calculating the sides of a scalene triangle

## How many equal sides does a scalene triangle have?

## Examples

Before we refer to the **scalene triangle**, it is important to know what a **triangle** itself is. The triangle is a **polygon** that has three different sides that are responsible for giving rise to three vertices and three internal angles. When we refer to a polygon, we refer to a **flat figure** that is delimited by different **segments**. Among the different kinds of polygons, there are triangles: polygons formed by three segments (sides). This is considered one of the simplest figures in the area of **geometry** and depending on its **sides**, can be classified into different types.

**Related topics**

Cathetus, hypotenuse, isosceles triangle, right triangle, Pythagoras

The scalene triangles are those triangles that have **three** different **sides**, each one of them with different **length**. In other words we can say that their **three sides** are **different**.

The main characteristics of scalene triangles are as follows:

- It is considered as a regular polygon that has three sides and because its sides are all of different size, but it can also be considered as a simple polygon because none of its points come together.
- The three
**sides**of the scalene triangle have**different measurements**. - They are triangles that house
**three interior angles**which are also all different. - It is also considered as a convex polygon.
- They are considered as some of the most
**resistant**geometric figures that exist in the area of geometry. - This type of geometric figure is considered to be the preferred figure to be used by many
**builders**and**architects**when standing any building. - It is important to mention that the term scalene is also used in geometry with reference to
**scalene trapezoids**which, like triangles of this type, have all their sides with different measurements. - When the scalene triangle is contained in a
**spherical surface**, it is known as a**spherical****triangle**. - The scalene triangle is also known as the
**unequal triangle**.

One of its most important properties are its sides because they have **lengths** of different measures, which is why in this type of triangle you can never show two **angles** that have the same measure.

When two of the sides of the scalene triangle are **summands**, the result obtained will always be greater than the length of the **third side**.

The scalene triangles have three different elements, and these are known by the name of **adjacent cathetus **to the angle, **opposite cathetus** to the angle and hypotenuse. These three elements are always present in a triangle. In addition to these, we can mention the interior of the triangle, which is the inner point of the triangle, the outer boundary which is constituted by the three sides of the triangle, the topological equivalence which says that any triangle will be equivalent to a simple closed curve. The topological equivalence.

The straight line that passes through the vertex of the triangle, the median that is the segment of straight line that goes from the vertex to reach the midpoint of the opposite side and the **perpendicular bisector** and circumscribed circumference, are three other elements that make up a scalene triangle.

Finally, within the elements of the triangle, the internal and external bisectors, the length of the bisector and the Steiner’s Theorem can also be mentioned.

The height can be calculated when a **side** (b) is known and the **height** (h) associated with that side.

**Area = (b – h) / 2**

Where b is the base and h is the height.

The area of a scalene triangle can be calculated by using **Heron’s formula**, if the **measurements** of all its sides (a, b and c) are known.

**Area = √ (s (s-a) (s-b) (s-c) )**

Where a, b and c are the three sides of the triangle and s the semi perimeter:

**s = (a+b+c) / 2**

The perimeter of a scalene triangle with three unequal sides is determined by adding the three sides.

**Perimeter = a + b + c**

Where a, b and c are the three sides of the triangle.

The **angles** that the scalene triangles have are completely **different** and there can never be a triangle within this classification, that has two of its sides of equal measure, they will always be different.

All **sides** of the scalene triangle should be measured using different mathematical **procedures**, as without these measurements it would be impossible to determine the perimeter of the scalene triangle.

Remember that scalene triangles do not have any of their **sides** of **equal measure** because if so, would be another type of triangle. Related to the sides of the scalene triangle we find the perimeter.

An example of a scalene triangle is as follows:

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Scalene triangle*. Recovered on 27 October, 2023, de Euston96: https://www.euston96.com/en/scalene-triangle/