The length and breadth of a hall are in the ratio 4 : 3 and its height is 5.5 metres. 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.

Given,

Ratio of length and breadth of a hall = 4:3

Let length of hall = 4x m

Let breadth of hall = 3x m

Height of hall = 5.5m (given)

So, lateral surface area of hall = 2(l+b)h =2(7x) ×5.5 = 77x m²

Cost of decorating walls = lateral surface area +rate of decoration per m²

= 5082 =

=

So, length of hall = 4x = 4×10 = 40 m

Breadth of hall = 3x = 3×10 = 30 m