Question

The dimensions of a room are $8m\times 6m\times h.$ It has two doors each of size $2m\times 1m$ and one almirah of size $3m\times 2m.$ The cost of covering the walls by wallpaper which is $40cm$ wide at $Rs.1.25$ per metre is $Rs.\mathrm{362.50.}$ Find height.

Answer 1

Given: Dimensions of a room are $8m\times 6m\times h.$

Dimensions of the two doors are $2m\times 1m$

The dimension of one almirah is $3m\times 2m.$

Area of the wall to be covered by wallpaper $=$ Area of fours walls $-$ (Area of 2 doors + area of $1$ almirah)

$=2h(8+6)-(2\times 2\times 1+3\times 2)$ [$\because$ Area of fours walls $=$ $2\times$height(length $+$ breadth), area of door $=$ lenght $\times$ breadth, Area of almirah $=$ length $\times$ breadth)]

$=28h-10$

Cost of covering the walls by wallpaper @ $Rs.1.25$ per metre $=Rs.362.50$

Total length of the wallpaper used $=Rs.\frac{362.50}{1.25}=290m$

Width of the wall paper $=40cm=0.40m$

Area of the wallpaper used $=$ (Total length $\times$ width) $=290\times 0.40=116m^2$

Area of the wall to be covered by wallpaper = Area of the wallpaper used

$28h-10=116$

$\Rightarrow 28h=116+10$

$\Rightarrow h=\frac{126}{28}=4.5m$

Hence, height of the room is $4.5m.$