Since the image gives that #bar(AC)# and #bar(DE)# are parallell, we know that #angle DEB# and #angle CAB# are equal.
Because two of the angles (#angle DEB# is a part of both triangles) in triangles #triangle ABC# and #triangle BDE# are the same, we know the triangles are similar.
Since the triangles are similar, the ratios of their sides are the same, which means:
#bar(AB)/bar(BC)=bar(BE)/bar(BD)#
We know #bar(AB)=22m# and #bar(BD)=4m#, which gives:
#22/bar(BC)=bar(BE)/4#
We need to solve for #bar(BE)#, but for us to be able to do that, we may only have one unknown. This means that we need to figure out #bar(BC)#. We can express #bar(BC)# in the following way:
#bar(BC)=bar(CD)+bar(BD)=12+4=16#
Now we can solve for #bar(BE)#:
#22/16=bar(BE)/4#
#22/16*4=bar(BE)/cancel4*cancel4#
#22/(4*cancel4)*cancel4=bar(BE)#
#bar(BE)=22/4#
So, #bar(BE)# must be #22 \/ 4\ m=5.5m#.
