Question

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

Answer 1

Find the length and breadth of the room.

$l:b=4:3$

Let the length, breadth and height of a room be $4x$, $3x$ and $5.5m$ respectively.

Rate of decorating wall $=₹6.60/m^2$

Total cost of decorating wall $=₹5082$

Total cost = area of the wall to be decorated $\times$ rate of decorating

$5082=2\left(lh+bh\right)\times 6.60$

$5082=2h\left(l+b\right)h\times 6.60$

$5082=2\times 5.5\left(4x+3x\right)\times 6.60$

$5082=11\left(7x\right)\times 6.60$

$5082=77x\times 6.60$

$77x=\frac{5082}{6.60}$

$77x=770$

$x=\frac{770}{77}$

$\therefore x=10$

Hence, the required length = $4\times 10=40m$ and Breadth = $3\times 10=30m$

Thus, the length and breadth of the room is $40m$and $30m$ respectively.