Scalene Triangle Math

Introduction :

A two dimensional geometric shape with three sides and angles is called as a triangle. If no sides and angles are equal in a triangle, then it is said to be as scalene triangle. i.e. a scalene triangle is formed by three different sides and angles. Here we are going to learn the math properties of scalene triangles.

Elements of a scalene triangle

Three angles:

`angle` ABC or `angle` B
`angle` ACB or `angle` C
`angle` CAB or `angle` A  and
Three sides:

AB
BC
CA
Types of scalene triangles in math

Acute scalene triangle
Obtuse scalene triangle
Right scalene triangle

Properties of scalene triangle in math

Definition

A scalene triangle is a triangle containing three unequal sides that all are of different lengths.Most triangles drawn at random would be scalene triangles.

Properties of Scalene triangles

A scalene triangle has no congruent sides.
no angles in a scalene triangle are equal.
Perimeter of a scalene triangle is given as
P = x + y + z where x,y,z are the sides of the triangle

a scalene triangle has no line of symmetry ( a line that divides the entire figure into two exact halves).
Calculation of area of a scalene triangle
Area of scalene triangle( that is a triangle with all different sides) can be calculated with the help of the following formula,

Area = `sqrt(s(s-a)(s-b)(s-c))`
where s = `(a+b+c)/(2)`  is the semi-perimeter, or half of triangle's perimeter.

Please express your views of this topic Perimeter of a Rectangle Formula by commenting on blog.

Example problems for scalene triangles in math

Example 1

Find the area of a scalene triangle with side lengths 4ft, 6ft, and 8ft respectively

Solution

Area = `sqrt(s(s-a)(s-b)(s-c))`

S = `(a+b+c)/2`

Here, a = 4ft

b = 5ft

c = 8 ft

So, s = `(4+5+8)/2`

= `17/2`

= 8.5

Area = `sqrt(8.5(8.5-4)(8.5-5)(8.5-8))`

= `sqrt(8.5xx 4.5 xx 3.5 xx 0.5)`

= `sqrt(66.937)`

= 8.181

So the area of the given scalene triangle = 8.181 square ft

Example 2

Find the perimeter of a scalene triangle with side lengths 4ft, 5ft and 8ft.

Solution

Perimeter of a scalene triangle = a + b + c

Here, a = 4, b = 5, and c = 8

Perimeter = 4 + 5 + 8

= 17 ft

So the perimeter of the given scalene triangle is 17 ft.