Question

A hall 36 m long and 24 m broad allowing 80 m² for doors and windows, the cost of papering the walls at Rs 8.40 per m² is Rs 9408. Find the height of the hall.

Answer 1

We have,
Length of the hall = 36 m
Breadth of the hall = 24 m
Let h be the height of the hall.
Now, in papering the wall, we need to paper the four walls excluding the floor and roof of the hall.
So, the area of the wall which is to be papered = Area of 4 walls
= 2h(l + b)
= 2h (36 + 24) = 120h m²
Now, area left for the door and the windows = 80 m²
So, the area which is actually papered = (120h − 80) m²
Again,
The cost of papering the walls at Rs 8.40 per m² = Rs. 9408.
⇒ (120h − 80) m² x Rs. 8.40 per m² = Rs. 9408

⇒ (120h − 80) m² = $\frac{\mathrm{Rs}.9408}{\mathrm{Rs}.8.40}$
⇒ (120h − 80) m² = 1120 m²
⇒ 120h m² = (1120 + 80) m²
⇒ 120h m² = 1200 m²

∴ h =$\frac{1200{\mathrm{m}}^2}{120\mathrm{m}}=10\mathrm{m}$
Hence, the height of the wall would be 10 m.