To find the height of the room, we will follow these steps:
### Step 1: Calculate the Total Area of the Walls
The total area of the walls of the room can be calculated using the formula for the area of the four walls of a rectangular room:
\[
\text{Total Area of Walls} = 2 \times (Length + Breadth) \times Height
\]
Given:
- Length = 7 m
- Breadth = 5 m
### Step 2: Calculate the Area of the Door and Windows
Next, we need to calculate the area of the door and the two windows to subtract from the total wall area.
**Area of the Door:**
\[
\text{Area of Door} = Length \times Breadth = 2 \, m \times 1.5 \, m = 3 \, m^2
\]
**Area of One Window:**
\[
\text{Area of One Window} = 1.5 \, m \times 1 \, m = 1.5 \, m^2
\]
**Area of Two Windows:**
\[
\text{Area of Two Windows} = 2 \times 1.5 \, m^2 = 3 \, m^2
\]
### Step 3: Calculate the Total Area of Openings
Now, we can find the total area of the openings (door + windows):
\[
\text{Total Area of Openings} = \text{Area of Door} + \text{Area of Two Windows} = 3 \, m^2 + 3 \, m^2 = 6 \, m^2
\]
### Step 4: Calculate the Effective Area to be Painted
Now, we can find the effective area to be painted by subtracting the area of openings from the total area of the walls.
\[
\text{Effective Area to be Painted} = \text{Total Area of Walls} - \text{Total Area of Openings}
\]
### Step 5: Calculate the Cost of Painting per Square Meter
Given that the total cost of painting is Rs. 5280 and the cost per square meter is Rs. 80, we can find the effective area to be painted:
\[
\text{Effective Area to be Painted} = \frac{\text{Total Cost}}{\text{Cost per m}^2} = \frac{5280}{80} = 66 \, m^2
\]
### Step 6: Set Up the Equation
Now we can set up the equation using the effective area to be painted:
\[
66 = 2 \times (7 + 5) \times h - 6
\]
### Step 7: Solve for Height (h)
First, simplify the equation:
\[
66 + 6 = 2 \times (12) \times h
\]
\[
72 = 24h
\]
\[
h = \frac{72}{24} = 3 \, m
\]
### Conclusion
The height of the room is **3 meters**.
---
