mjhjmtu

I can not get the attached figure.

documentclass[tikz,11pt,border=5mm]standalone
usepackagetikz
usepackagegeometry
usetikzlibrarypositioning,calc,intersections


begindocument

begintikzpicturethick,x=0.5cm,y=0.5cm

coordinate [label=below left : $A$](A) at (0,0);
coordinate [label=below right : $B$](B) at (10,0);
coordinate [label=above left : $C$] (C) at (0,5);

path[name path=line1] (C.east) -- (C.east-|B.west)coordinate[pos=0.6](N) ;
path[name path=line2] (A) -- (B);
path[name path=line3]($(A)!(N)!(B)$) -- (N);
path[name path=line4]($(C)!(N)!(A)$) -- (N);
path[name path=line5] (A) -- (C);

path[name intersections=of=line1 and line3,by=P];
path[name intersections=of=line1 and line5,by=M];

draw[fill=green] (A-|P) --(N) -- (C-|M) -- (A) --cycle;
draw (A)--(B)--(C)--cycle;

node[above] at (N)$N$;
node[below] at (P)$P$;

endtikzpicture

enddocument

Similar to @Sigur but there are no intersections used (as not needed).

documentclass[tikz,11pt,border=5mm]standalone
usetikzlibrarypositioning,calc


begindocument

begintikzpicture[thick,x=0.5cm,y=0.5cm]
coordinate [label=below left : $A$](A) at (0,0);
coordinate [label=below right : $B$](B) at (10,0);
coordinate [label=above left : $C$] (C) at (0,5);
path (C) -- (B)coordinate[pos=0.6,label=above right:$N$](N) ;
draw[fill=green] (A) rectangle (N);
coordinate[label=above left:$M$] (M) at (A|-N);
draw (A) -- (B) -- (C) -- cycle;
endtikzpicture
enddocument

Output as your desired screen shot.

Just control the position of P between A and B. I used 60%.

documentclass[tikz,11pt]standalone
usetikzlibrarypositioning,calc,intersections

begindocument

begintikzpicture[thick,x=0.5cm,y=0.5cm]

coordinate [label=below left : $A$](A) at (0,0);
coordinate [label=below right : $B$](B) at (10,0);
coordinate [label=left : $C$](C) at (0,5);
coordinate [label=below : $P$](P) at ($(A)!.6!(B)$);

path[name path=hipo] (C) -- (B);
path[name path=rightVertical] (P) -- (P|-C) ;
path[name path=leftVertical] (A) -- (C);

path[name intersections=of=rightVertical and hipo,by=N];
path[name path=horizontal] (N) -- (N-|C) ;
path[name intersections=of=horizontal and leftVertical,by=M];

draw[fill=green] (P)--(N)--(M)--(A)--cycle;
draw (A)--(B)--(C)--cycle;
node[above] at (N)$N$;
node[left] at (M)$M$;
endtikzpicture

enddocument