Three forces P, Q and R are acting on A, B and C respectively.
P, Q and R are parallel.
P/a = Q/b = R/c = k
Net force through the center of the triangle = P+Q+R = P(1+Pb/a+Pc/a)
= (a+b+c)P/a = (a+b+c) k
Net force is proportional to the perimeter of the triangle. It is in the same direction as the parallel forces P, Q and R.
As there are multiple forces acting on the triangle at different points, there will be a net Torque on the triangle and So the triangle ABC will rotate.
Let the angle made by P, Q and R with the side is Ф. Then the net torque about the axis perpendicular to the plane of ABC and passing through G (centroid) is :
= d_P Χ P + d_R Χ Q + d_R Χ R , where d_P, d_Q and d_R are perpendicular lengths from G onto P, Q and R respectively.
net torque = [ P (a + b - 2c) Sin Φ - R (b + c - 2 a) Sin (B-Φ) ] / 3
If the triangle is free to move and rotate, then it will translate with the net force and the instantaneous torque is given by above formula.