Question

A room is half as long as it is broad. The cost of carpeting the room at Rs $3.25m^2$ is Rs $175.50$ and the cost of preparing the walls at Rs$1.40$ per sq.m is Rs$240.80$. If $1$ door and $2$ windows occupy $8m^2$, then find the dimensions of the room ?

Answer 1

Let the breadth of the room be $a$m

$\Rightarrow$ Length of the room$=a+\frac{a}{2}=\frac{3a}{2}$m

Area of the room$a\times \frac{3a}{2}=\frac{3a^2}{2}$sq.m

$\Rightarrow$ Cost of carpeting the room at Rs.$3.25$per sq.m$=$Rs.$3.25\times \frac{3a^2}{2}$

$\Rightarrow 75.50=3.25\times \frac{3a^2}{2}$

$\Rightarrow a^2=\frac{175.50\times 2}{3.25\times 3}=36$

$\Rightarrow a=6$

$\Rightarrow$ Breadth$=a=6$m and length$=\frac{3\times 6}{2}=9$m

Let the height of the room be $h$m

Area of $4$ walls$=2(l+b)\times h=2(6+9)\times h=30h$sq.m

Area of $1$ door and $2$ windows$=8$sq.m

Area to be papered$=$Area of $4$ walls$-$Area of $1$ door and $2$ windows

$=(30h-8)$sq.m

$\Rightarrow$Cost of papering walls at Rs.$1.40$per sq.m$=$Rs.$(30h-8)\times 1.40$

$\Rightarrow 240.80=(30h-8)\times 1.40$

$\Rightarrow 30h-8=\frac{240.80}{1.40}=172$

$\Rightarrow 30h=172+8=180$

$\Rightarrow h=\frac{180}{30}=6$m

Hence, dimensions of the room are

Length$=9$m, Breadth$=6$m and Height$=6$m