Given A room is half as long again as it is broad
Let the breadth of the room x m
length of the room x + x/2 = 3x/2m
Area of the room , x × 3x/2 = 3x²/2m
Given , cost of carpeting the room at Rs. 3.25m⁻²
So , total cost , 3x²/2 × 3.25
But , Total cost of carpeting is given as 175.50 so ,
- (3x²/2 )× 3.25 = 175.50
- x² = 175.50 × 2 / 3.25 × 3
- x² = 36
- x = 6
- Breadth x = 6 m
- length 3x/2 = 9m
let the height of the room H m
Area of the four wall = 2(L+ b)× h 2(6+9)× H
= 30H m²
Area of the of the one door and two window is 8m²
8m² Area to be prepared = Area of four wall - area of two window and 1 door = (30H - 8) m²
Given cost of preparing wall is Rs. 1.40m²
total cost of preparing wall is (30H - 8) × 1.40
Total cost of preparing wall is given as 240.80
comparing , (30H - 8 ) × 1.40 = 240.80
- (30H - 8 ) = 240.80 /1.40 = 172
- 30H -. 8 = 172
- 30H = 180
- H = 180/30 = 6
Hence, Dimensions of the room are lengths 9m , breadth 6m and height 6m