Question

Area of an equilateral triangle is 24 root 3 cm square. What will be its perimeter?

Answer 1

area of equilateral triangle = √3×a²/4 where a is the side of the triangle
24√3 = √3a²/4
24 = a²/4
a =4√6
perimeter of equilateral triangle = 3a = 12√6 cm

Answer 2

Let the side of equilateral triangle be x.

Area of equilateral triangle = √3/4 * x²
∴24√3 = √3/4 * x²
∴24 = x²/4
∴24 * 4 =x²
∴96 = x²
∴16 * 6=x²
∴x = 4√6 cm.

Now, perimeter of the equilateral triangle = 3*x = 3*4√6 = 12√6 cm