Outside perimeter = AH+DH+DG+BG+BF+EF+EJ+CJ+CI+AI = 50
Pentagon perimeter = HG+GH+FJ+JI+IH = 30
Adding these two equations
(AH+DH+DG+BG+BF+EF+EJ+CJ+CI+AI) + (HG+GH+FJ+JI+IH) = 50 + 30
Rearranging them,
(AH+HG+BG)+(BF+FJ+CJ)+(CI+IH+DH)+(DG+GF+EF)+(EJ+AI+JI) = 80
that is AB+BC+CD+DE+EA=80