Question 79

Let G be the centroid of the equilateral triangle ABC of perimeter 24 cm. Then the length of AG is

Solution

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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