Question

The length and breadth of a hall are in the ratio $4:3$ and its height is $5.5m$ . The cost of decorating its walls (including doors and windows) at $Rs.6.60$ per square metre is $Rs.5082$. Find the length and breadth of the room.

Answer 1

Given: Cost of decorating $4$ walls of the room at $Rs.6.60$ per square metre is $Rs.5082$.

Therefore, Area of the $4$ walls = $\frac{\text{Total cost of decorating 4 walls}}{\text{Cost of decorating per square metre}}=\frac{5082}{6.60}=770m^2$

Now, let length of the wall ($l$) = $4x$

Breadth of the wall ($b$)= $3x$ and

Height of the wall ($h$)= $5.5m$

Hence, area of $4$ walls = $2\times hb+2\times hl=2h\times (l+b)$

Now ATQ,

$\Rightarrow 2h\times (l+b)=770$

$\Rightarrow 2\left(5.5\right)\times \left(7x\right)=770$

$\Rightarrow x=\frac{770}{2\times 5.5\times 7}=10m$

Hence, length of the wall = $4\times 10=40m$ and

Breadth of the wall = $3\times 10=30m$