Mathematics

Scalene Triangle

we have different types of triangles from which Scalene Triangle is a geometric figure or irregular polygon which has three sides with each of different measures and an axis of symmetry. hence, their consequent angles will also be unequal or of different lengths. even in some cases, the right triangles are also said to be scalene triangles when their angles and sides are not congruent.

in short, “the scalene triangle is one formed by three sides and three different angles to each other”.

Scalene Triangle

the perimeter of such type triangle can be found by adding up all the sides and by the sum of its internal angles add up to 180º (α + β + γ = 180º).

What are the Elements of the scalene triangle?

  • Sides: AB, BC, AC, are three sides that measure a, b, and c, respectively.
  • Vertices: it has three vertices like A, B, and C.
  • Interior Angles: we say x, y, z are interior angles which result in 180º by adding them up.
  • Exterior Angles: we say α, β, and γ are exterior angles that are supplementary to the same side’s interior angle. (α + β= β+ γ=γ +α= 180º)

Area of Scalene Triangle

we can find the area of such a triangle by using Heron’s formula.
A=b.h/2
where, a=area, b=base and h=height
By Using Heron’s formula:
Area of a scalene triangle
In this case, we are based on Heron’s formula where s is the semi perimeter. That is P / 2.
Where a, b, and c are the measurements of the sides of the triangle and p given by the formula:
p: semi-perimeter of the scalene triangle

The perimeter of the Scalene Triangle

as we knew the specific triangle also has three sides as other types of triangles. to find the perimeter, we need to sum all three sides. so,

Perimeter= a+b+c

if two sides and their adjacent angle are known, we can use the perimeter by using the cosine theorem.

finding perimeter using cosine theorem

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