The area of an equilateral triangle and area of square are in the ration √3 : 2. If the length of diagonal of square is 60 cm. let us write by calculating perimeter of that triangle.

Area of equilateral triangle = ,

Where, x is the equal side of triangle

Area of square = side × side

Let side of square here be x cm

In a square the diagonal is hypotenuse

Diagonal = hypotenuse = √ 2 a

According to the given condition

60 = √ 2a

⇒

⇒ a = 30√2

⇒ Area of square = (30√2 )² = 3600 ………….eq1

Given

From eq 1

⇒ Area of equilateral triangle = 1800√ 3cm

But Area of equilateral triangle =

⇒ 1800√ 3 =

⇒

⇒ 84.85 = x cm

Perimeter of the equilateral triangle = 3x

= 3 × 84.85

= 254.56 cm