Question

Centroidal distance of an equilateral triangle with side 'a' from any of the three sides is​

Answer 1

Step-by-step explanation:

is just a very simple matter. Let the equilateral triangle be OAB where O be the origin of the Co-ordinate plane and side OA = a ( say ) lies on the positive direction of x- axis, side OB (= a ) making an angle of 60 degree with x- axis . Then the three vertices O , A & B of the triangle have their co-ordinates respectively as : (0, 0 ) , ( a, 0 ) & ( aCos60⁰, aSin60⁰) . Therefore the centroid G (g, h ) also the incenter I of the triangle OAB is given by;

g = (1/3) [ 0 + a + aCos60⁰]

= (1/3) [ a + a/2 ] =3a /6 .