Question

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 m’ is 15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area.]​

Answer 1

Given :

• Perimeter of the floor of a rectangular hall = 250 m
• Cost of painting the four walls at the rate of 10 per m² = Rs. 15000

To find :

• Height of the hall

Knowledge required :-

→ Formula of area of four walls :-

• Area of four walls = 2(l + b)h

→ Formula of perimeter of rectangle :-

• Perimeter = 2(l + b)

where,

• l = length
• b = breadth

Solution :

Perimeter of the floor = 2(l + b) = 250 m

Area of four walls = 2(l + b)h = (250)h = 250h m²

Area of four walls = 250h m²

Cost of painting 1 m² of the wall = Rs. 10

Cost of painting 250h m² of the wall = 10 × 250h = Rs. 2500h

But, cost of painting the four walls = Rs. 15000

So,

⠀⠀⠀⇒ 15000 = 2500h

⠀⠀⠀⇒ 15000/2500 = h

⠀⠀⠀⇒ 150/25 = h

⠀⠀⠀⇒ 6 = h

★ Therefore, height of the hall = 6 m