Question : If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, $\angle$BGC = $120^{\circ}$, BC = 10 cm, then the area of the triangle ABC is:

Option 1: $50\sqrt{3}$ $cm^2$

Option 2: $60$ $cm^2$

Option 3: $25$ $cm^2$

Option 4: $25\sqrt{3}$ $cm^2$

Question : In $\Delta$ABC, D is the mid-point of BC and G is the centroid. If GD = 5 cm then the length of AD is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 15 cm

Option 4: 20 cm

Question : In $\triangle$ABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm.The length of median AD (in cm) is:

Option 1: 4.5

Option 2: 5

Option 3: 4

Option 4: 3

Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

Option 1: 6

Option 2: 5

Option 3: 4.5

Option 4: 12

Question : If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19 cm and AC = 22 cm then the length of BC is:

Option 1: 19.5 cm

Option 2: 26 cm

Option 3: 20.5 cm

Option 4: 13 cm