Question : The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:
Option 1: $2 \sqrt{3}\ \text{cm}$
Option 2: $4 \sqrt{3}\ \text{cm}$
Option 3: $5 \sqrt{3}\ \text{cm}$
Option 4: $3 \sqrt{3}\ \text{cm}$
Correct Answer: $2 \sqrt{3}\ \text{cm}$
Solution :
Given: The centroid of an equilateral triangle PQR is L.
If PQ = 6 cm, the height of the equilateral triangle $=\frac{\sqrt{3}}{2} ×\ \text{side}=\frac{\sqrt{3}}{2} × 6 = 3\sqrt{3} \ \text{cm}$
Also, the centroid divides the height of the triangle into 2 : 1 ratio.
So, $PL = \frac{2}{3}×3\sqrt{3}$
$⇒PL = 2\sqrt{3}\ \text{cm}$
Hence, the correct answer is $2\sqrt{3}\ \text{cm}$.
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