Here is the triangle.  Let b represent the base.
Then since the legs are 4 cm longer than b, they are
b+4 each:




The perimeter is just the measurement all the way around the RIM
of of the triangle.  [Notice that the word "RIM" is inside the word
"peRIMeter"].

Perimeter = LEFT LEG + RIGHT LEG + BASE = 44cm.  So

              (b+4)  +  (b+4)    +   b  = 44

                      b + 4 + b + 4 + b = 44

                                 3b + 8 = 44
                                     -8   -8
                               --------------
                                 3b     = 36

                                     = 

                                      b = 12

So the base is 12cm.

Edwin