The floor of a rectangular hall has a perimeter 250 m . If the cost of painting the four walls at the rate of rupes 10 per ` m^(2)` is rupes 15,000 , find the height of the hall.

Answer

To find the height of the hall, we can follow these steps:

### Step 1: Understand the given information
We are given:
- The perimeter of the rectangular hall is 250 m.
- The cost of painting the four walls is ₹15,000 at the rate of ₹10 per m².

### Step 2: Use the perimeter formula
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + B) \]
Where \( L \) is the length and \( B \) is the breadth of the hall. Given that the perimeter is 250 m, we can write:
\[ 2(L + B) = 250 \]
Dividing both sides by 2 gives:
\[ L + B = 125 \] (Equation 1)

### Step 3: Calculate the area of the four walls
The cost of painting the four walls is given as ₹15,000. Since the cost per m² is ₹10, we can find the total area of the four walls:
\[ \text{Total area} = \frac{\text{Total cost}}{\text{Cost per m²}} = \frac{15000}{10} = 1500 \, m² \]

### Step 4: Write the formula for the area of the four walls
The area of the four walls of the hall can be calculated using the formula:
\[ \text{Area} = 2H(L + B) \]
Where \( H \) is the height of the hall. We know from Equation 1 that \( L + B = 125 \). Therefore, we can substitute this into the area formula:
\[ 2H(125) = 1500 \]

### Step 5: Solve for the height (H)
Now we can solve for \( H \):
\[ 250H = 1500 \]
Dividing both sides by 250 gives:
\[ H = \frac{1500}{250} = 6 \, m \]

### Conclusion
The height of the hall is 6 meters.

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