Question : G is the centroid of a triangle ABC, whose sides AB = 35 cm, BC = 12 cm, and AC = 37 cm. The length of BG is (corrected to one decimal place):
Option 1: 11. 7 cm
Option 2: 12.9 cm
Option 3: 17.5 cm
Option 4: 12.3 cm
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Correct Answer: 12.3 cm
Solution :
G is the centroid of a $\triangle$ABC
AB = 35 cm
BC = 12 cm
AC = 37 cm
$\triangle$ABC is a right-angled triangle with $\angle B = 90^{\circ}$
Point G is on BD.
BD = circumradius
Circumradius = $\frac{\text{hypotenuse}}{2}$
⇒ BD = $\frac{37}{2}$
Also, BD = BG + GD
and BG : GD = 2 : 1
$\therefore$ BG = $\frac{2}{3}$ × BD = $\frac{2}{3} × \frac{37}{2}$ = $\frac{37}{3}$ = 12.33 cm
Hence, the correct answer is 12.3 cm.
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