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Let width of carpet be 'x'm Therefore, inclusive of border: Length of room = 8m Breadth of room = 5m Length of carpet = 8-x-x = (8-2x)m Breadth of carpet = 5-x-x = (5-2x)m

Area of room (carpet + border) = 8*5 = 40sq.m

Area of just carpet = (8-2x)(5-2x) = (40-16x-10x+4x^2) = (4x^2-26x+40)sq.m

Area of just border = 12sq.m (given)

Therefore, Area of ground = Area of just border + Area of just carpet => 40 = 12+(4x^2-26x+40) => 0 = 4x^2-26x+12 => 0 = 2x^2-13x+6 (dividing equation by 2) => 0 = 2x^2-12x-x+6 => 0 = 2x(x-6)-1(x-6) => 0 = (2x-1)(x-6) => x = 1/2 = 0.5m or 6m