Question 897667
Given that the area of an equilateral triangle is 192 cm2, find its perimeter.

Note: Your answer must be a number. No arithmetic operations are allowed.

Can you explain to me how I do this exercise? 

Thanks 
<pre>
Let each side of triangle be S
Since a 30-60-90 right triangle exists, and the hypotenuse is: S, then the base is: {{{S/2}}}, and the altitude is: {{{(S*sqrt(3))/2}}}
Now, since the area is {{{192_cm^2}}}, we can say that: {{{(1/2)(S/2)(S*sqrt(3)/2) = 192}}}_____{{{(S^2sqrt(3))/8 = 192}}}
{{{S^2sqrt(3) = 8(192)}}} ------- Cross-multiplying
{{{S^2 = 8(192)/sqrt(3)}}}
{{{S^2 = (8(192)sqrt(3))/(sqrt(3)*sqrt(3))}}} ----- Rationalizing denominator
{{{S^2 = (8(192)sqrt(3))/3}}}
{{{S^2 = (8(64cross(192))sqrt(3))/cross(3)}}}
{{{S^2 = 512sqrt(3)}}}
{{{S = sqrt(512sqrt(3))}}}

Perimeter: 3S, or {{{3sqrt(512sqrt(3))}}}
You can do the check!! 

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