Q. 34.0( 418 Votes )

# 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]

Answer :

**Given:** Perimeter of the floor of hall = 250 m, Cost of painting the four walls = Rs. 15, 000**To Find:** Height of the hall

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

**Area of four walls = 2lh + 2bh = 2(l + b) h**

**Perimeter of the floor of hall = 2(l + b)**

Perimeter of the floor of hall = 250 m

Therefore, 2(l + b) = 250 m

Putting this value in the formula of Area of four walls we get,

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

**Area of four walls = 250h m ^{2}**

Cost of painting per m^{2} area = Rs 10

Cost of painting 250h m^{2} area = Rs (250h × 10)

= Rs 2500h

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

15000 = 2500h

h = 6

**Therefore, the height of the hall is 6 m**

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