The length of a room is one and a half times its breadth. The cost of carpeting the room at `R s .3.25\ p e r\ m^2\ i s\ R s .175.50` and the cost of papering the walls at `R s .1.40\ p e r\ m^2i s\ R s .240.80` . If 1 door and 2 window occupy `8\ m^2,` find the dimensions of the room.

Explanation

Let the breadth of room` b`.
Then length of the room is` 1.5b`.
area carpeted`=frac { 175.50 }{ 3.25 } m^ 2 =54 m ^ 2`
area of floor`=54m^ 2`
` lxxb=54`
`1.5 b ^ 2=54`
` b ^ 2=frac { 54 }{ 1.5 } =36`
` b=sqrt 36 =6m quad & quad l=1.5 quad b=9m`
area whitewashed`=frac { 240 }{ 1.4 } =172 m ^ 2`
`172=`area of walls-total area of one door and two windows
`172=2(l+b)h-8`
`2(9+6)h-8=172`
`:.l=9m, b=6m ,h= 6m`