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 m2 is ₹15000, find the height of the hall.


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Answer 1

Answer:

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=15000/2500

⇒h=6m

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Answer 2

Solution :-

$\boxed{Area\:of \:the\:four\:walls\:=\:Lateral\: surface\:area}$

A rectangular hall means a cuboid.

Let the length= L

and, breadth = B

∴ Perimeter of the floor = 2(l + b)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⇒ 2(l + b)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 250 m

∵ Area of four walls = Lateral surface area

⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 2(1 + b) x h

( where h is the height of the hall)

⠀⠀⠀⠀⠀⠀⠀⠀ = 250h ${m}^{2}$

Cost of painting the four walls :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⇒ Rs. (10 x 250 h)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⇒ Rs. 2500h

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⇒ 2500 h = 15000

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⇒ h = $\dfrac{15000}{2500}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 6

Thus, the required height of the hall = 6 m