I'm assuming the heavy length segments are the outer shape of the diagram.

Have a look at the attached diagram.

let say the perimeter of the overlap (which is a triangle) = a + b + c = 3.

when both rectangles (rectangle 1 on the left, and rectangle 2 on the right) do not overlap, their respective perimeters are 12 and 12.

when they overlap, part of the perimeter of rectangle 1 is 'lost'. This lost section is c. the same way, part of perimeter of rectangle 2 is lost. This lost section of rectangle 2 is a+b.

So the perimeter of the diagram = (12 - c) + (12 - b - a)
= 24 - a - b - c
= 24 - (a + b + c)
= 24 - 3
= 21

Choose C.

-BM-

OA is C

I liked ur approach, BM

-BM-