Area of four walls of a room is `168 m^2`. The breadth and height of the room are 8 m and 6 m respectively. The length of the room is :

Options

A. 14m
B. 12m
C. 3.5m
D. 6m

Answer

To find the length of the room, we can use the formula for the area of the four walls of a room, which is given by:

\[ \text{Area of four walls} = 2 \times \text{height} \times (\text{length} + \text{breadth}) \]

Given:
- Area of four walls = 168 m²
- Breadth (B) = 8 m
- Height (H) = 6 m

Let's denote the length of the room as \( L \).

### Step 1: Write the formula for the area of the four walls
\[ 168 = 2 \times H \times (L + B) \]

### Step 2: Substitute the known values into the formula
\[ 168 = 2 \times 6 \times (L + 8) \]

### Step 3: Simplify the equation
Calculating \( 2 \times 6 \):
\[ 168 = 12 \times (L + 8) \]

### Step 4: Divide both sides by 12 to isolate \( (L + 8) \)
\[ \frac{168}{12} = L + 8 \]
\[ 14 = L + 8 \]

### Step 5: Solve for \( L \)
Subtract 8 from both sides:
\[ L = 14 - 8 \]
\[ L = 6 \, \text{m} \]

Thus, the length of the room is **6 meters**.

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