The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs. 10 per \({m}^2\) is Rs.15000, find the height of the hall.
[Hint : Area of the four walls = Lateral surface area.]

Let the length, breadth, and height of the rectangular hall be l m, b m, and h m respectively.

Now, perimeter of the floor of hall
= 2(l + b) = 250 m ...(Given)

Also, Area of four walls = 2lh + 2bh
\(\Rightarrow \) Area of four walls = 2(l + b)h = 250 h \({m}^2\)

Now, Cost of painting per \({m}^2\) area = Rs. 10

\(\therefore \) Cost of painting 250 h area = Rs. (250h x 10) = Rs. 2500h

However, it is given that the cost of painting the walls is Rs 15000.

Hence, 15000 = 2500h
\(\Rightarrow \) h = \(\frac{15000}{2500}\)
\(\Rightarrow \) h = 6

Therefore, the height of the hall is 6 m.