Q. 174.0( 8 Votes )

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.

Answer :

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


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