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

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 : 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 : In $\triangle ABC$, D and E are the midpoints of sides BC and AC, respectively. AD and BE intersect at G at the right angle. If AD = 18 cm and BE=12 cm, then the length of DC (in cm ) is:

Option 1: 10

Option 2: 6

Option 3: 9

Option 4: 8

Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.

Option 1: 18 cm

Option 2: 16 cm

Option 3: 20 cm

Option 4: 22 cm