Question

the floor of a rectangular hall has a perimetrr 250 m. if the cost of painting the four walls at the rate of rupees 10 per m2 is rupees 15000, find the height of the hall.

Answer 1

Perimeter of rectangular hall = 2(l + b) = 250 m

Total cost of painting = Rs.15000

Rate per m² = Rs.10

Area of four walls = 2(l + b) h m² = (250×h) m²

A/q,

(250×h)×10 = Rs.15000

⇒ 2500×h = Rs.15000

⇒ h = 15000/2500 m

⇒ h = 6 m

Thus the height of the hall is 6 m.

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Answer 2

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 ${m}^{2}$ is ₹15000, find the height of the hall.

Given ::-

• Perimeter of rectangle = 250m

• Cost of painting four walls at the rate of 10 per ${m}^{2}$ = ₹15000

To find ::-

• Height of hall..?

Solution ::-

A rectangular hall is cuboid.

Let ,

• Length = l
• 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 isthe 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