Question : AD is the median of $\triangle \mathrm{ABC}$. G is the centroid of $\triangle \mathrm{ABC}$. If AG = 14 cm, then what is the length of AD?
Option 1: 42 cm
Option 2: 28 cm
Option 3: 35 cm
Option 4: 21 cm
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Correct Answer: 21 cm
Solution :
AD is the median of triangle ABC.
G is the centroid of triangle ABC.
If AG = 14 cm
So, $\frac{AG}{GD}=\frac{2}{1}$
⇒ $\frac{14}{GD} = \frac{2}{1}$
⇒ $GD =7$ cm
$\therefore$ AD = AG + GD = 14 + 7 = 21 cm
Hence, the correct answer is 21 cm.
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