The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is

A) \$2\sqrt{2}\$

B) \$3\sqrt{2}\$

C) \$2\sqrt{3}\$

D) \$\sqrt{3}\$

In a \$\triangle\$ABC, AB = 10cm, BC=12cm and A = 14cm. Find the length of median AD. If G is the centroid, find length of GA.

A) \$4\sqrt{7}, \frac{8}{3}\sqrt{7}\$

B) \$5\sqrt{7}, 4\sqrt{7}\$

C) \$4\sqrt{7}, \frac{10}{\sqrt{7}}\$

D) \$43sqrt{7}, 3\sqrt{7}\$

ABC is a equilateral traingle and P is the centroid. If the side of the triagngle is 12cm, then what is the length of PA.

A) \$ 4\sqrt{3} \$

B) \$ 2\sqrt{3} \$

C) \$ 8\sqrt{3} \$

D) \$ 16\sqrt{3} \$

The area of a triangle is 72 square units. Find the length of the altitude if the length of the base is 9 units.

A) \$10\$ units

B) \$16\$ units

C) \$12\$ units

D) \$13\$ units

Find the height an isosceles triangle ABC with two sides of length 5 and one side of length 8.

A) \$14\$

B) \$6\$

C) \$10\$

D) \$12\$