(i) A footpath of uniform width runs all around the inside of a rectangular field 54 m long and 35m wide. If the area of the path is 420 m^2, find the width of the path.
(ii) A carpet is laid on the floor of a room 8m by 5m. There is a border of constant width all around the carpet. If the area of the border is 12 m^2, find its width.