Question 181165
Formula: If a triangle is equilateral of side <i>s</s>, then the altitude is {{{(s sqrt(3))/2}}}

Here, the altitude is given as 12 cm.

Let s=side of the triangle.
Then,
{{{(ssqrt(3))/2=12}}}
{{{ssqrt(3)=24}}}
{{{s=24/sqrt(3)}}}
This is not the answer yet. We have to rationalize the denominator. Let's multiply the right side by {{{sqrt(3)/sqrt(3)}}}

{{{s=(24/sqrt(3))(sqrt(3)/sqrt(3))=(24sqrt(3))/3=8sqrt(3)}}}

The equilaterla triangle has three congruent sides. Therefore, the perimeter,
P={{{3(8sqrt(3))=24sqrt(3)}}}cm

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