Question

8. The floor of a rectangular hall has a perimeter 15 m.
If the cost of painting the four wall at the rate of 10 per m^2 is 15000, find the height of the hall.
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Answer 1

Question -

The floor of a rectangular hall has a perimeter of 15 m. If the cost of painting the four wall at the rate of 10 per m ² is 15000,find the height of the hall.

Solution -

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

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

$15 = 2(l + b)$

$l + b = \frac{15}{2}$

$l + b = 7.5........1)$

Area of four walls = Area of cuboid - Area of floor - Area of top

Area of four walls = 2(lb+bh+lh)-lb- lb

Area of four walls= 2(lb)+2(bh)+2(lh)-2(lb)

Area of four walls= 2(lh)+2(bh)

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

Area of four walls= 2h ×7.5 [by 1)]

Area of four walls= 15hm²

Now,

Cost of painting per m²= Rs 10

Cost of painting 15 h m²= Rs 10×15h

$15000 = 150h$

$h = \frac{15000}{150}$

$h = 100m$

Therefore the height of the hall is 100m

Answer 2

Question -

• The floor of a rectangular hall has a perimeter of 15 m. If the cost of painting the four wall at the rate of 10 per m ² is 15000

Find:-

• The height of the hall.

Step by step explanation

Let length be l, Breadth be b, Height be h respectively.

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

15 = 2 (l + b)

$( l+ b) = \frac{15}{2}$

l + b = 7.5

Area of four walls = Area of cuboid - Area of floor - Area of top

Area of four walls = 2(lb+bh+lh)-lb- lb

Area of four walls= 2(lb)+2(bh)+2(lh)-2(lb)

Area of four walls= 2(lh)+2(bh)

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

Area of four walls= 2h ×7.5 [by 1)]

Area of four walls= 15hm²

Now,

Cost of painting per m²= Rs 10

Cost of painting 15 h m²= Rs 10×15h

15000 = 150h

$h = \frac{15000}{150} \\ h = 100$

H = 100mh=100m

Hence, the height of the hall is 100m