JEE Main & Advanced Mathematics Statistics Triangle Theorem of Couples

If three forces acting on a body be represented in magnitude, direction and line of action by the sides of triangle taken in order, then they are equivalent to a couple whose moment is represented by twice the area of triangle.

Consider the force P along AE, Q along CA and R along AB. These forces are three concurrent forces acting at A and represented in magnitude and direction by the sides BC, CA and AB of DABC. So, by the triangle law of forces, they are in equilibrium.

The remaining two forces P along AD and P along BC form a couple, whose moment is, \[m=P.AL=BC.AL\]

 Since, \[\frac{1}{2}(BC.AL)\] = Area of the \[\Delta ABC\]

\[\therefore \]Moment \[=BC.AL=2\](Area of \[\Delta ABC\]).