Question

ABC is an equilateral triangle of side 12 cm. If G be its centroid, find AG.

Answer 1

centroid AG=4 root 3cm

Answer 2

in tri ABD
by Pythagoras theoram
$ab { }^{2} = bd {}^{2} + ad {}^{2}$
$ad {}^{2} = {ab {}^{2} } - bd {}^{2}$
$ad {}^{2} = 12 ^{2} - 6 {}^{2}$
$ad {}^{2} = 144 - 36$
$ad {}^{2} = 108$
$ad = \sqrt{108}$
$ad = 6 \sqrt{3}$
$ag = \binom{2}{3} ad$
$ag = \binom{2}{3} \times 6 \sqrt{3}$
$ag = 2 \times 2 \sqrt{3}$
$ag = 4 \sqrt{3}$cm
it will help you