The area of the four walls of a room is `660 m^(2)` and its length is twice its breadth. If the height of the room is 11 m, then area of its floor (in `m^(2)`) is

Options

A. 120
B. 150
C. 200
D. 330

Answer

To find the area of the floor of the room, we can follow these steps:

### Step 1: Understand the given information
We know that:
- The area of the four walls of the room is \( 660 \, m^2 \).
- The height of the room \( H \) is \( 11 \, m \).
- The length \( L \) is twice the breadth \( B \) (i.e., \( L = 2B \)).

### Step 2: Use the formula for the area of the four walls
The formula for the area of the four walls of a room is given by:
\[ \text{Area of four walls} = 2H(L + B) \]
Substituting the known values, we have:
\[ 660 = 2 \times 11 \times (L + B) \]

### Step 3: Simplify the equation
First, calculate \( 2 \times 11 \):
\[ 660 = 22(L + B) \]
Now, divide both sides by \( 22 \):
\[ L + B = \frac{660}{22} = 30 \]

### Step 4: Substitute \( L \) in terms of \( B \)
Since \( L = 2B \), we can substitute this into the equation:
\[ 2B + B = 30 \]
This simplifies to:
\[ 3B = 30 \]

### Step 5: Solve for \( B \)
Now, divide both sides by \( 3 \):
\[ B = \frac{30}{3} = 10 \, m \]

### Step 6: Find \( L \)
Now, using \( L = 2B \):
\[ L = 2 \times 10 = 20 \, m \]

### Step 7: Calculate the area of the floor
The area of the floor is given by:
\[ \text{Area of floor} = L \times B = 20 \times 10 = 200 \, m^2 \]

### Final Answer
The area of the floor is \( 200 \, m^2 \).

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