A frame structure ABCD as shown below is fixed at A$.$A trapezoidal distributed force is applied on the section BC of the frame structure. A cable is attached at point E and run through a frictionless pulley attached on the frame structure at point D$.$ The cable is then pulled with a force P in an orientation shown in the figure below. Calculate the reactions at the fix support A$.$

Please use this numerical information in your calculation: L $=4$ m$,$ w$1=20$ N$/$m$,$ w$2=10$ N$/$m$,$ P $=100$ N$.$