To determine the cost of carpeting the room, we first need to calculate the area of the room that needs to be carpeted.
The area of the room is:
A = l × w
A = 6 m × 4 m
A = 24 square meters
Next, we need to determine the area of the carpet required. Since the carpet has a width of 1.5 m, we can think of the room as being covered by a series of strips of carpet, each of width 1.5 m. We need to calculate the length of each strip and then multiply that by the width of the carpet.
The length of each strip is equal to the length of the room, which is 6 m. So, the area of each strip of carpet is:
A_strip = l × w_carpet
A_strip = 6 m × 1.5 m
A_strip = 9 square meters
To cover the entire room, we will need to use several strips of carpet. The number of strips required is the total area of the room divided by the area of each strip:
Number of strips = A / A_strip
Number of strips = 24 square meters / 9 square meters
Number of strips = 2.6667 strips
Since we cannot use a fractional number of strips, we will need to round up to 3 strips of carpet.
The total area of carpet required is the area of each strip multiplied by the number of strips:
Total area of carpet = A_strip × Number of strips
Total area of carpet = 9 square meters × 3
Total area of carpet = 27 square meters
Finally, we can calculate the cost of carpeting the room at the given rate of rupees 200 per meter:
Cost of carpeting = Total area of carpet × Cost per meter
Cost of carpeting = 27 square meters × Rs. 200 per meter
Cost of carpeting = Rs. 5,400
Therefore, the cost of carpeting the rectangular room of 6 m long and 4 m wide with the carpet of width 1.5 m at rupees 200 per meter would be Rs. 5,400.