Question

The centre of gravity of an equilateral triangle with each side a, is __________ from any of the three sides.
A.3a/2
B.23a
C. a/23
D.32a

Answer 1

Answer:

a/(2√3)

Explanation:

The centre of gravity of an equilateral triangle with each side a, is __________ from any of the three sides.

Center of gravity will divide Triangle into three equal triangle

Distance of this point from any side will be perpendicular distance from side

let say distance = d

and side of equilateral triangle = a

Area of Equilateral Triangle = (√3 / 4)a²

Area of any one internal triangle with one side & centre of gravity

= (1/2) a * d

there are three such triangles

so total area = (3/2)ad

(3/2)ad = (√3 / 4)a²

=> 3d = (√3 / 2)a

=> d = ( 1/2√3)a

=> d = a/(2√3)

The centre of gravity of an equilateral triangle with each side a, is a/(2√3) from any of the three sides.