Q. G is the centroid in the equilateral △ ABC. If AB = 10 cm then length of AG is :
Answer: $latex \frac{10\sqrt{3}}{3}cm&s=1$
Notes: AB = 10cm BD = 5 cm ∠ADB = 90° ∴ AD = $latex \sqrt{AB^{2} - BD^{2}}$ $latex => \sqrt{10^{2}-5^{2}} = \sqrt{100-25}$ $latex => \sqrt{75} = 5\sqrt{3}cm$ $latex AG =$ $latex \frac{2}{3}&s=1$ $latex AD=$ $latex \frac{2}{3}\times 5\sqrt{3}&s=1$ $latex = \frac{10\sqrt{3}}{3}cm&s=1$ Hence option [C] is the right answer.