Question : The length of the altitude of an equilateral triangle is $6 \sqrt{3}\;m$. The perimeter of the equilateral triangle (in m) is:
Option 1: $12 \sqrt{2}$
Option 2: $36 \sqrt{2}$
Option 3: $36$
Option 4: $24 \sqrt{3}$
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Correct Answer: $36$
Solution :
Let $a$ be the side of an equilateral triangle.
Altitude of an equilateral triangle is $6 \sqrt{3}\;m$.
Since altitude $=\frac{\sqrt 3 a}{2}$
So, $6 \sqrt{3} = \frac{\sqrt 3 a}{2}$
⇒ $a = 6×2 = 12$ m
Therefore, the perimeter = $3a = 3×12 = 36$ m
Hence, the correct answer is $36$.
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