To find the length of paper required, we need to calculate the total area of the walls and ceiling that need to be covered.

The area of the walls can be calculated by finding the perimeter of the room and multiplying it by the height. The perimeter of the room is 2 times the sum of the length and width.

Perimeter of the room = 2 * (7m + 5m) = 2 * 12m = 24m

Area of the walls = Perimeter of the room * height = 24m * 3.5m = 84m²

The area of the ceiling is simply the length multiplied by the width.

Area of the ceiling = Length * Width = 7m * 5m = 35m²

Now, we need to find the total area that needs to be covered by the paper.

Total area = Area of the walls + Area of the ceiling = 84m² + 35m² = 119m²

Since the paper is 6 dm wide, we need to convert the width to meters.

Width of the paper = 6 dm = 6/10 m = 0.6 m

To find the length of paper required, we divide the total area by the width of the paper.

Length of paper required = Total area / Width of the paper = 119m² / 0.6m = 198.33m

Since we cannot buy a length less than a meter, we round up the length to the nearest meter.

Length of paper required = 199m

Therefore, the length of paper required is 199 meters.