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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Question : ABC is an equilateral triangle. If the area of the triangle is $36 \sqrt{3}$, then what is the radius of the circle circumscribing the $\triangle ABC$?
Question : Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is:
Question : $\triangle ABC$ is an equilateral triangle with a side of 12 cm and AD is the median. Find the length of GD if G is the centroid of $\triangle ABC$.
Question : In an isosceles triangle, the length of each equal side is twice the length of the third side. The ratios of areas of the isosceles triangle and an equilateral triangle with the same perimeter are:
Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?
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