A hall $36 m$ long and $24 m$ broad allowing $80 m^{2}$ for doors and windows , the cost of preparing the walls at $R s . 8.40$ per $m^{2}$ is $R s 9408$ . Find the height of the hall.

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Solution

Length of hall = 36 m ; breadth of hall = 24 m
Let 'h' be height of the hall
Now in preparing the wall, we need to paper the four walls excluding floor and root of the hall.
so area of wall which is to be papered
$= l h + b h + l h + b h = 2 h (l + b) = 2 h (36 + 24) = 120 h m^{2}$
Now area leaves for doors and windows $= 80 m^{2}$
so the area which is actually papered $= (120 h - 80) m^{2}$
Again cost of papering the walls at Rs. 8.40 per $m^{2}$
is equal to Rs 9408.
$(120 h - 80) \times 8.4 = 9408$
$120 h - 80 = 1120 \Rightarrow 120 h = 1200 \Rightarrow h = 10 m .$

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