If the area on an equilateral triangle is 81 root 3 . find it’s perimeter

Area  = 1/2 * base + height  = 81 √3

Find the relation between the base and the height:-

The triangle formed by the perpendicular from a vertex to the base  is a 30-60-90 triangle  where the ratio of its sides is 2:1:√3   where 2 is hypotenuse, height is √3 and  1 = 1/2 base of the equilateral triangle. So here we can let 1/2 base = x then height = √3x.

So 81 √3 = x * √3x

x^2 = 81

and x = 9  and the hypotenuse = 2*x = 2x

Therefore the perimeter =  2x * 3

= 6*9

= 54    answer

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