Question

The length of a room is $3$ times its height and breadth is $1\frac{1}{2}$ times its height. The cost of whitewashing the wall at the rate of $Rs1.50$ $per$ $sq.m.$ is $Rs216.$ Find the dimensions of the room.

Answer 1

Let h be the height of the room

so length $=3$h

Breadth $=\frac{3}{2}$h

Area of walls $=2(lh+bh)$

Area of walls $=\frac{cost}{Rate}=\frac{216}{1.50}=144m^2$

So $2h(3h+\frac{3}{2}h)=144$

$\Rightarrow 2h\left(\frac{9h}{2}\right)=144$

$\Rightarrow h^2=\frac{144}{9}\Rightarrow h=\frac{12}{3}=4m$

$l=12$ m, $b=6$ m, $h=4$ m.