Question

if an area of an equilateral triangle is 81square root 3. find it's perimeter

Answer 1

Area of equilateral  triangle = √3/4 x a²
√3/4 x a² = 81√3

a²/4 = 81 

a² = 81 x 4 

a² = 324

a = 18 

perimeter = 3 x 18 = 54 (unit)

Answer 2

Hey Friend !!!

This is your answer.

It is given that the area of equilateral triangle = 81√3 unit².

Also, area of equilateral triangle is $\frac{ \sqrt{3} }{4} l^{2}$.

So, 

$81 \sqrt{3} = \frac{ \sqrt{3} }{4} l^2 \\ =\ \textgreater \ l^{2} =81 X4 \\ =\ \textgreater \ l= \sqrt{81 X 4} \\ =\ \textgreater \ l=9X2 \\ l=18$

Hence, side of equilateral triangle is 18 units.

Now,
We know that perimeter of equilateral triangle 
= 3 X side 
= 3 X 18
= 54 units.

Hence, the perimeter of given triangle is 54 units.

Hope it helps You...