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# 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.