The ratio of sides of a triangle is 3 : 4 : 5 and area of the triangle is 72 squares unit. The the area of an equilateral triangle whose perimeter is same as that of the previous triangle is

Explanation:

Let the sides be 3x, 4x and 5x

⇒area =1/2×3x×4x=72

⇒6x^2=72

x^2=12

x=2√3

⇒ Perimeter of equilateral △

=12×2√3

=24√3units

Side of△=24√3/3

=8√3–√units

area of △=√3/4×(8√3)^2

=√3/4×64×3=48√3unit^2