Question

the floor of a rectangular hall has a perimeter 250m.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 with a rectangular hall = 250 m

Cost of painting the four walls at the rate of 10 per m² = Rs. 15000

To Find :-

The height of the hall.

Solution :-

We know that,

• l = Length
• b = Breadth
• h = Height
• a = Area

According to the question,

Area of four walls = 2lh + 2bh

= 2 (l + b) h

Given that,

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

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

Cost of painting per square meter = Rs. 10

Then,

Cost of painting 250h square meter area = Area of four walls × Cost of painting per square meter

Substituting their values,

Cost of painting 250h square meter = 250h × 10

Cost of painting = Rs.2500h

In the question,

Given that, the cost of paining the walls is Rs. 15000

15000 = 2500h

h = 6

Therefore, the height of the hall is 6 m

Answer 2

Step-by-step explanation:

Given:

Perimeter=250m

⇒Area of 4 walls =2lh+2bh

=2(b+l)h

⇒Perimeter of floor of wall =2l+2b

⇒2(l+b)=250 m

∴ Area of 4 walls =2(l+b)h

=250h m

2

⇒Cost of painting per m

2

area = Rs. 10

⇒Cost of painting 250h m

2

area = Rs(250h×10)

= Rs.2500h

⇒Painting cost of walls = Rs. 15000

⇒2500h=15000

⇒h=

2500

15000

⇒h=6m