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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 ₹ 15,000, find the height of the hall.
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Solution
Let the length, breadth, and height of the rectangular hall be l m, b m, and h m respectively.
The perimeter of the floor of hall = 2(l + b)
250 m = 2(l + b)
(l + b) = `250/2 = 125` cm ...(i)
Area of four walls = Area of cuboid – Area of floor – Area of top
= 2 (lb + bh + hl) – (l x b) – (l x b)
= 2(lb) + 2 (bh) + 2(hl) – 2lb = 2 lh + 2 bh
= 2h(l + b)
= 2h x 125 [From (i)]
= 250h m2
Area of four walls = 250h m2
Cost of painting 1 m2 area = ₹ 10
Cost of painting 250h m2 area = ₹ 10 x 250h = 2500h
15000 = 2500h
h = `15000/2500`
The height of the hall is 6 m.
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