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Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is
equilateral triangle ABC of perimeter 24 cm
let a be side of $$\triangle ABC$$
perimeter = 3a = 24
a = 8
height of the equilateral triangle = $$\frac{\sqrt{3}}{2}a$$ = $$\frac{\sqrt{3}}{2}\times 8$$ = $$4\sqrt{3}$$
centroid divides the height in 2:1
length of AG = $$\frac{2}{3} $$height of equilateral traingle = $$\frac{2}{3}\times 4\sqrt{3}$$
$$\frac{8}{\surd3}$$ cm
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