Question

the area of an equilateral triangle is 2 root 3 cm square find its perimeter​

Answer 1

Step-by-step explanation:

Given :-

The area of an equilateral triangle is 2 √3 cm²

To find :-

Find its perimeter ?

Solution :-

Let the side of an equilateral triangle be X cm

Area of an equilateral triangle = (√3/4)X² cm²

According to the given problem

The area of an equilateral triangle = 2 √3 cm²

=> (√3/4)X² = 2√3

=> X² = 2√3×(4/√3)

=> X² = (2√3×4)/√3

=> X² = 2×4

=> X = √(2×4)

=> X = √(2×2×2)

=> X = 2√2 cm

The side of the equilateral triangle = 2√2 cm

We know that

Perimeter of an equilateral triangle = 3X cm

=> 3×2√2 cm

=> Perimeter = 6√2 cm

Answer:-

Perimeter of the equilateral triangle = 6√2 cm

Used formulae:-

→ Area of an equilateral triangle = (√3/4)a² sq.units

→ Perimeter of an equilateral triangle = 3a units

• a = Side of the equilateral triangle