Equiangular Triangle

Equiangular triangle is the triangle in which all the three angles are equal to each other. Since sum of all the angles in a triangle always should add up to 180º, hence when we add three equal angles to 180º, we get each angle as 60º. Therefore in an equiangular triangle, each angle measures 60º. Since all the angles are equal to each other, according to triangle properties all the sides are also equal in measure. So in an equiangular triangle, the sides and the angles are of equal measure.

Example 1: What is the length of each side of an equiangular triangle, if the perimeter of the triangle is 48m?
Given: Perimeter of the triangle, P = 48m

Perimeter of a triangle = Sum of all the sides of the triangle.

Let each side of the triangle be = x and since it’s an equiangular triangle, all the sides are equal!

Then x + x + x = 48==> 3x = 48

This gives: x= 48/3 = 16m

Hence the length of each side of the given triangle = 16m.

Example 2: If the length of a side of an equiangular triangle is 4m, then what is the perimeter of the triangle?

Given: length of each side of the triangle = 4m

Perimeter of a triangle = Sum of all the sides of the triangle.

Since it’s an equiangular triangle, all the sides are equal!

Hence we get:Perimeter of the triangle, P = 4 + 4 + 4 ==>Perimeter = 12m

Therefore perimeter of the given triangle, P = 12m

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