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Carpet Repairs

Carpet has lifted from where carpet joins kitchen tiles. It has detached and is fraying. The distance of the edge that needs to be repaired is 101cm. Unless someone can suggest a better solution, I was thinking of perhaps screwing in a carpet edging strip over the top of the carpet to hold it down. I can see there is wood underneath to screw into but I am not sure how deep it is before it reaches the concrete floor.