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Question

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


Solution

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 = Total cost of decorating 4 wallsCost of decorating per square metre=50826.60=770 m2

Now, let length of the wall (l) = 4x 

Breadth of the wall (b)= 3x and

Height of the wall (h)= 5.5 m

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

Now ATQ,

2h×(l+b)=770

2(5.5)×(7x)=770

x=7702×5.5×7=10 m

Hence, length of the wall = 4×10=40 m and 

Breadth of the wall = 3×10=30 m


Mathematics
RD Sharma
Standard IX

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