A room is half as long again as it is broad. The cost of carpeting the room at `Rs 13` per `m^(2)` is `Rs 702` and the cost of papering the walls at `Rs 7` per `m^(2)` is `Rs 1204.` If `1` door and `2` window occupy `8 m^(2)`, find find dimensions of the room

Explanation

Let the breadth of the room be `x` metres
Then, its length `= (x + (x)/(2))` metres `= (3x)/(2)` metres
Area of the floor `= (l xx b) = ((3x)/(2) xx x) m^(2) = (3x^(2))/(2) m^(2)`
Also, area of the floor `= ("total cost of carpeting")/("rate per "m^(2))`
`= ((702)/(13)) m^(2) = 54 m^(2)`
`:. (3x^(2))/(2) = 54 rArr x^(2) = (54 xx (2)/(3)) = 36 = (6)^(2) rArr x = 6`
`:.` breadth = 6m and length `= ((3)/(2) xx 6) m = 9m`
Area of papered walls `= ("total cost of papering")/("rate per " m^(2))`
`= (1204)/(7) m^(2) = 172 m^(2)`
Area of 1 door and 2 windown `= 8 m^(2)`
Area of 4 walls `= (172 + 8) m^(2) = 180 m^(2)`
Let the height of the room be h metres
Then, area of 4 walls `= {2 (l + b) xx h} = {2 (9 + 6) xxh} m^(2)`
`= (30h) m^(2)`
`:. 30h = 180 rArr h = (180)/(30) = 6m`
Hence, length = `9m`, breadth = `6m` and height = `6m`.