Question

Ex 13.1 Class 9 Maths Question 3. 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 ₹15000, find the height of the hall. [Hint: Area of the four walls = Lateral surface area]​

Answer 1

Answer :

• The height of the hall is 6m

Given :

• 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 ₹15000,

To Find :

• The height of the hall. [Hint: Area of the four walls = Lateral surface area]

Solution :

• Let the length be l
• Let the breadth be b
• Let the height be h

Given

• Perimeter is 250m

As we know that :

• Perimeter = 2(l + b)

Where,

• l is length
• b is breadth

⇢ Perimeter = 2(l + b)

⇢ 250 = 2(l + b)

⇢ l + b = 250/2

⇢ l + b = 125 ... (1)

We know that

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

Where,

• Area of cuboid is 2(lb + bh + lh)
• Area of top is l × b
• Area of floor is l × b

⇢ 2(lb + bh + lh) - lb - lb

⇢ 2(lb) + 2(bh) + 2(lh) - 2(lb)

⇢ 2lh + 2bh

⇢ 2h(l + b)

⇢ 2h × (l + b)

⇢ 2h × 125 (equation 1) because l + b = 125

⇢ 250hm²

Area of four walls is 250h m²

Finding the height of the hall :

• Cost of painting per 1m² = Rs.10
• Cost of painting per 250 h m² Rs.10 × 250h = 2500h

And also Given,

The cost of painting the four walls at the rate Rs.10 per m² is Rs. 15000 so,

⇢ 15000 = 2500h

⇢ h = 15000/2500

⇢ h = 6m

Hence ,

The height of the hall is 6m