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Scalene Triangle

What is a Scalene triangle?

Scalene triangles are a special type of triangles in geometry. They are defined as triangles with three unequal sides and three unequal angles. This means most triangles drawn at a random would be scalene. Scalene Triangle Picture In the above figure, all the three sides and all the three internal angles of the triangle are different. Thus, it is a scalene triangle. Let’s understand scalene triangles in a bit more detail.

Properties of Scalene Triangle

  • Has no congruent side.
  • Has no equal angle.
  • Has no line of symmetry.

Types of Scalene Triangle

There are mainly four types of Scalene triangle:-

  • Acute Scalene Triangle – A triangle where all the three angles are acute angles (less than 90o), and all the three sides are of different lengths.
  • Obtuse Scalene Triangle – A triangle where one of the internal angles are obtuse (more than 90o) and all the three sides are of different length.
  • Right Scalene Triangle – A triangle where one of the angles is right angle (exactly 90o) and all the three sides are of different length.
  • Special Scalene Right Triangle – A triangle where all three sides are of different length and the internal angles are 30o, 60o and 90o.

How to find the area of a scalene triangle?

Area of a triangle is referred to as the total space confined within its borders. It is denoted in terms of square unit. Formula The area of a scalene triangle can be simply calculated using the given formulas:
Area = \frac{1}{2} \times a \times b                     [where b = base, h = height] If all the sides of the triangle are known they apply this: Area = \sqrt{s(s-a)(s-b)(s-c)}           [where s = \frac{a+b+c}{2} ]

 Scalene Triangle Area  

h (height) is calculated by dropping a perpendicular to the base. This means, any side can be taken as base, but a line forming 90omust be dropped on it. The length of this line is the height (as shown in figure).
 Scalene Triangle Area Pictures  

If the base has an obtuse angle, then we extend the base and drop a perpendicular forming 90o with that line to find the height (as shown in figure).

How to find the perimeter of a scalene triangle?

The perimeter of a triangle is defined as the total distance around the edge of the triangle. Or in short, just adding up the three sides will give us the perimeter of the triangle. Formula

 Perimeter = a + b + c                [where a, b, c are the given sides]

Examples

Q1) Which of these 2 triangles is a scalene triangle? Image of ScaleneTriangle Solution – Option (b) – Because all of its sides are of different length.

Q2) Now let’s try solving a mathematical problem based on scalene triangles. Solution Step 1 – The sides of the triangle are given. AB = 10cm; BC = 14cm; AC = 8cm.

 Scalene Triangle Question  

Given is a triangle with sides 8cm, 10cm and 14cm. Find the Area and Perimeter of the triangle.

Step 2 – The formula to calculate Area of a triangle is: Area = \sqrt{s(s-a)(s-b)(s-c)}  [where s = \frac{a+b+c}{2} ] [a, b, c are the length of three sides AB, BC and AC].

Step 3 – Substituting the respective values: s = \frac{10+14+8}{2} = \frac{32}{2} = 16}

Step 4 – Hence, Area = \sqrt{16(16-10)(16-14)(16-8)} = \sqrt{16 (6)(2)(8)} = \sqrt{16 (96)} = \sqrt{1536} = 39.16cm The Area of the triangle is 39.19 cm.

Step 5 – As we know, the formula to find perimeter of a triangle is:  Perimeter = a + b + c, where a, b, c are the given sides of the triangle.

Step 6 – Substituting with given values:   Perimeter = 10 + 14 + 8. Or, Perimeter = 32 cm.

Solution – The Perimeter of the triangle is 32 cm.


Published by on May 24th 2014. Filed under Math Facts

 

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