The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m² is ₹ 15,000, find the height of the hall.

Given:

Perimeter of the floor of the rectangular hall = 250 m

Total cost of painting the four walls = ₹ 15,000

Rate of painting = ₹ 10 per m²

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

Perimeter of floor = 2(l + b)

⇒ 2(l + b) = 250

⇒ l + b = $\dfrac{250}{2}$

⇒ l + b = 125 ……………(1)

The total cost of painting the four walls equals to the curved surface area of the rectangular hall.

Total cost = Curved surface area of hall x Rate of painting

⇒ 15,000 = Curved surface area x 10

⇒ Curved surface area = $\dfrac{15,000}{10}$

⇒ Curved surface area = 1,500 m²

Curved surface area of hall = 2(l + b)h

⇒ 1,500 = 2(l + b)h

Using equation (1),

⇒ 1,500 = 2 x 125 x h

⇒ 1,500 = 250 x h

⇒ h = $\dfrac{1500}{250}$

⇒ h = 6

Hence, the height of the rectangular hall is 6 m.