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We can classify triangles according to the length of their sides and the measures of their angles.
Equilateral triangle
A triangle is called an equilateral triangle if all three of its sides are equal and its angles are equal as well (60° each).
Isosceles triangle
An isosceles triangle is a triangle that has two equal sides and two equal angles.
Scalene triangle
Before we dive into the in-depth definition, a scalene triangle is a triangle that has no equal sides. None of its three sides are equal to each other and it has no equal angles either. In this article, we are going to discuss the definition, properties and formulas of a scalene triangle.
What is a scalene triangle?
In geometry, triangles are defined based on their sides and angles. A triangle is a closed plane three-sided polygon figure with three sides and three angles. A scalene triangle has sides with varying lengths. They are unequal and its angles are of three different measures. However, the sum of its angles remains 180°, just like all triangles.
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Properties of a scalene triangle
The scalene triangle has a few important properties that are exclusive to it:
– The sides of the triangle are unequal
– All of its angles are different
– It has no line of symmetry
– It has no point symmetry
– The angles of a scalene triangle can be acute, obtuse or right
– The angle opposite of the longest side of a scalene triangle is the greatest angle and the angle opposite to the shortest side is the smallest angle
– If the scalene triangle is acute (meaning all its angles are less than 90°), then the circumcenter is inside of the triangle
– On the other hand, if the scalene triangle is obtuse (it has an angle that is more than 90°), the middle of the circumscribing will be outside the triangle
– The scalene triangle can be right-angled, obtuse-angled or acute-angled
Formulas of a scalene triangle
When it comes to a scalene triangle, there are two main formulas to always keep in mind: the perimeter and the area.
The area
The area of a scalene triangle is half of the base multiplied by the triangle’s height.
The formula is:
A = (1/2) x b x h
Where: b = the distance of the base of the triangle
h = the height of the triangle
Example:
We have a scalene triangle with a base of 20 cm and a height of 12 cm.
Therefore the area of this triangle is :
A = (1/2) x 20 x 12 = 120 cm
The perimeter
The perimeter of a scalene triangle is the sum distance around the edge of the triangle or the sum of the length of the sides.
The formula is:
P = a + b + c
Example:
We have a scalene triangle and the lengths of its three sides are 30 cm, 25 cm and 17 cm respectively.
So, the perimeter of this triangle is :
P = 30 + 25 + 17 = 72 cm
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A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures. Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent.
Example 1:
In the triangle shown, all the three sides have different lengths.
Example 2:
In the triangle shown, all the three angles have different measures.
A scalene triangle is a triangle that has three unequal sides, such as those illustrated above.