Question

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 m2 is Rs. 15,000, find the height of the hall.

Answer 1

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

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 = Rs. 10

Cost of painting 250h m2 area = Rs. 10 x 250h = 2500h

15000 = 2500h

h = 15000/2500

The height of the hall is 6 m.