The perimeter's edge (3)
I believe the answer is:
rim
I believe this is a double definition.
'the perimeter's' is the first definition.
(I've seen this in another clue)
'edge' is the second definition.
(I know that rim is a type of edge)
(Other definitions for rim that I've seen before include "Raised edge of a round object" , "Flange" , "Top edge" , "Edge or margin" , "'Brim, lip (3)'" .)