The area of an equilateral triangle is 432√3

Solution

ATQ, Area of equilateral triangle = (√3/4) X side² Let the side of the given triangle be 'a' cm. ATQ; 432√3 = (√3/4) X a² Or, 432 X 4 = a² So, 'a' = ± 24√3 Since, side cannot be negative, a = +24√3 Height of equilateral triangle = (√3/2) X side So, height of the given triangle = (√3/2) X 24√3 = 36 cm So, length of each side of the square = 36 cm So, perimeter of the square = 36 X 4 = 144 cm And perimeter of the triangle = 24√3 X 3 = 72√3 cm So, required difference = 144 - 72√3 = 72(2 - √3) cm