Question : PQR is an equilateral triangle and the centroid of triangle PQR is point A. If the side of the triangle is 12 cm, then what is the length of PA?
Option 1: $4 \sqrt{3}$ cm
Option 2: $8 \sqrt{3}$ cm
Option 3: $2 \sqrt{3}$ cm
Option 4: $\sqrt{3}$ cm
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Correct Answer: $4 \sqrt{3}$ cm
Solution :
Given: PQR is an equilateral triangle and the centroid of triangle PQR is point A. The side of the triangle is 12 cm. The equilateral triangle circumradius = $\frac{\text{side}}{\sqrt3}$. The equilateral triangle's centres are all located at the same point. Whether it's a centroid, incentre, orthocentre, or circumcentre. The length of PA = $\frac{PQ}{\sqrt3}$. $=\frac{12}{\sqrt3}=4\sqrt3$ cm Hence, the correct answer is $4\sqrt3$ cm.
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