ABC is an equilateral triangle with side 24 cm and AD is the median. If G is the centroid of the triangle ABC, find the length (in cm) of GD.
4\(\sqrt3\)
Median of an equilateral triangle with side a: \(\dfrac{\sqrt3}{2}a\). With a=24: \(\dfrac{\sqrt3}{2}\times24 = 12\sqrt3\) cm.
The centroid divides the median in the ratio 2:1 from the vertex, so GD (from centroid to the base) is one-third of the median: \(\dfrac{12\sqrt3}{3} = 4\sqrt3\) cm.
Hence, the length of GD is \(4\sqrt3\) cm.
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