what is Equilateral Triangle and prove its formula ?

 

Definition of an Equilateral Triangle

An equilateral triangle is a triangle where all three sides are of equal length. Let's denote the length of each side of the equilateral triangle as $𝑠$.

Perimeter of a Triangle

The perimeter of a triangle is the total length around the triangle, which is the sum of the lengths of all its sides.

Calculating the Perimeter of an Equilateral Triangle

Since an equilateral triangle has all three sides of equal length, the perimeter $𝑃$ is simply three times the length of one side.

Mathematically, this can be expressed as:

$𝑃=𝑠+𝑠+𝑠$

Since all sides are the same length, we can rewrite this as:

$𝑃=3𝑠$

Conclusion

So, the formula for the perimeter of an equilateral triangle with side length $𝑠$ is:

$\boxed{{\displaystyle 𝑃=3𝑠}}$

This formula is derived from the fact that all three sides of an equilateral triangle are equal and thus the perimeter is just three times the length of one side.