Final answer:
To calculate the cost of carpeting a rectangular room where the length is twice the width and the perimeter is 36m, we determine the room's dimensions, calculate the area, and then multiply by the rate. The width is 6m, the length is 12m, giving an area of 72m². The total carpeting cost at Rs.250 per square meter is Rs.18000.
Step-by-step explanation:
To find the cost of carpeting a room, we need to know the room's dimensions and then calculate its area. Given that a room is twice as long as it is broad and has a perimeter of 36m, we can set up two equations to find the length and width. Let the width be x meters, then the length is 2x meters.
The perimeter of a rectangle is calculated by P = 2(l + w), where l is the length and w is the width. Using the given perimeter of 36m, we get 36 = 2(2x + x). Solving this equation, we find x=6 meters, so the width is 6m and the length is 12m. The area of the floor is l × w, which gives us 72m².
Finally, to find the cost of carpeting at the rate of Rs.250 per square metre, we multiply the area by the rate, giving us a total cost of Rs.18000 (72m² × Rs.250/m²).