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Sum

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^{2} 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 m^{2}

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

Cost of painting 1 m^{2} area = ₹ 10

Cost of painting 250h m^{2} area = ₹ 10 x 250h = 2500h

15000 = 2500h

h = `15000/2500`

The height of the hall is 6 m.

Concept: Surface Area of a Cuboid

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