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

Question : $\triangle ABC$ is an equilateral triangle with a side of 12 cm and AD is the median. Find the length of GD if G is the centroid of $\triangle ABC$.

Option 1: $6 \sqrt{3}$ cm

Option 2: $3 \sqrt{3} $ cm

Option 3: $4 \sqrt{3} $ cm

Option 4: $2 \sqrt{3}$ cm

Question : In $\triangle A B C,\ D$ is the mid-point of $BC$ and $G$ is the centroid. If $G D = 10\ \text{cm} $, the length of $AD$ is_____.

Option 1: 20 cm

Option 2: 30 cm

Option 3: 15 cm

Option 4: 10 cm

Question : The centroid of a $\triangle ABC$ is G. The area of $\triangle ABC$ is 60 cm². The area of $\triangle GBC$ is:

Option 1: 10 cm²

Option 2: 30 cm²

Option 3: 40 cm²

Option 4: 20 cm²

Question : $\triangle ABC \sim \triangle DEF$ and the perimeters of $\triangle ABC$ and $\triangle DEF$ are 40 cm and 12 cm respectively. If DE = 6 cm then AB is:

Option 1: 12.6 cm

Option 2: 24 cm

Option 3: 20 cm

Option 4: 10 cm