A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per sq.m is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.
Correct Answer: Option A
Let breadth = x metres, length = 3x metres, height = H metres.
Area of the floor=(Total cost of carpeting)/(Rate) = (270/5) sq.m = 54 sq.m
\(x\times\frac{3x}2=54\Rightarrow x^2=54\times2\Rightarrow x=6\)
So, breadth = 6 m and length = \(\frac{3\left(6\right)}2\)
= 9 m.
Now, papered area = (1720/10) = 172 sq.m
Area of 1 door and 2 windows = 8 sq.m
Total area of 4 walls = (172 + 8) sq.m = 180 sq.m
\(2\times\left(9+6\right)H=180\Rightarrow H=6\)
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