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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