Question : AD is the median of triangle ABC. P is the centroid of triangle ABC. If AP = 14 cm, then what is the length of PD?
Option 1: 14 cm
Option 2: 28 cm
Option 3: 21 cm
Option 4: 7 cm
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Correct Answer: 7 cm
Solution : AD is the median of triangle ABC. P is the centroid of triangle ABC. If AP = 14 cm The centroid of the triangle divides each of its medians in the ratio 2 : 1. ⇒ $\frac{\text{AP}}{\text{PD}} = \frac{2}{1}$ ⇒ $\frac{14}{\text{PD}} = \frac{2}{1}$ ⇒ $\text{PD} = \frac{14}{2}$ $\therefore$ PD = 7 cm Hence, the correct answer is 7 cm.
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