Question:A room is half as long again as its is broad. The cost of carpeting the room at Rs.5 per sq.m. is Rs.270 and the of papering the four walls at Rs.10 per `m^2` is Rs. 1720. If a door and 2 windows occupy 8 sq. metres, find the dimensions of the room. 

Answer Let the breadth = x metres & length` = (3x)/2` metres.

Area of the floor` = ((Total cost of carpeting)/(Rate|m^2)) m^2`

                    `= (270/5) m^2`

                   `= 54 m^2`


`:. x xx (3x)/2 = 54 or x^2`

`= 54 xx 2/3 = 36 or x = 6`

:. Breadth = 6 m & length` = (3/2 xx 6) m`

                   `= 9 m`

Now, papered area` = (1720/10) m^2`

                     `= 172 m^2`

Area of 1 door and 2 windows` = 8m^2`

Total area of 4 walls` = (172 + 8) m^2`

                  `= 180 m^2`

`:. 2 (length + breadth) xx height = 180`

`or 2 (9 + 6) xx H = 180 or H = (180/30)`

`= 6 m` 

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