Certainly! Let's find the height of the room step-by-step given the information about the area of the four walls, length, and breadth.
### Given Data:
- Area of the four walls of the room: [tex]\( \text{Area}_{walls} = 210 \, \text{m}^2 \)[/tex]
- Length of the room: [tex]\( L = 12 \, \text{m} \)[/tex]
- Breadth of the room: [tex]\( B = 9 \, \text{m} \)[/tex]
### Formula to Use:
The formula for the area of the four walls of a room, when the height is [tex]\( H \)[/tex], is:
[tex]\[ \text{Area}_{walls} = 2 \cdot H \cdot (L + B) \][/tex]
### Rearranging the Formula:
To find the height [tex]\( H \)[/tex], we can rearrange the formula:
[tex]\[ H = \frac{\text{Area}_{walls}}{2 \cdot (L + B)} \][/tex]
### Step-by-Step Solution:
1. Calculate the sum of length and breadth:
[tex]\[ L + B = 12 \, \text{m} + 9 \, \text{m} = 21 \, \text{m} \][/tex]
2. Calculate the denominator in the fraction for height:
[tex]\[ 2 \cdot (L + B) = 2 \cdot 21 \, \text{m} = 42 \, \text{m} \][/tex]
3. Find the height using the formula:
[tex]\[ H = \frac{\text{Area}_{walls}}{2 \cdot (L + B)} = \frac{210 \, \text{m}^2}{42 \, \text{m}} \][/tex]
4. Perform the division:
[tex]\[ H = \frac{210}{42} = 5 \, \text{m} \][/tex]
### Conclusion:
The height of the room is [tex]\( 5 \, \text{m} \)[/tex].
