The area of the 4 walls of a room is `168 m^(2)`. The breadth and height of the room are 10 m and 4 m respectively. Find the length of the room.

Answer

To find the length of the room given the area of the four walls, breadth, and height, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Area of the Four Walls:**
The area of the four walls of a room can be calculated using the formula:
\[ \text{Area} = 2 \times (L + B) \times H \]
where \( L \) is the length, \( B \) is the breadth, and \( H \) is the height of the room.

2. **Substitute the Known Values:**
We know the area of the four walls is \( 168 \, m^2 \), the breadth \( B = 10 \, m \), and the height \( H = 4 \, m \). Substituting these values into the formula gives:
\[ 168 = 2 \times (L + 10) \times 4 \]

3. **Simplify the Equation:**
First, simplify the right-hand side:
\[ 168 = 8 \times (L + 10) \]

4. **Divide Both Sides by 8:**
To isolate \( L + 10 \), divide both sides by 8:
\[ L + 10 = \frac{168}{8} \]
Calculate \( \frac{168}{8} \):
\[ L + 10 = 21 \]

5. **Solve for Length \( L \):**
Now, subtract 10 from both sides to find \( L \):
\[ L = 21 - 10 \]
Thus,
\[ L = 11 \, m \]

### Final Answer:
The length of the room is \( 11 \, m \).

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