The total area of four walls of a room is `660 m^2` and the length is twice its width. If the height of the room is 11m, then the area of its ceiling is

Options

A. `200 m^2`
B. `150 m^2`
C. `100 m^2`
D. `75 m^2`

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
We know that:
- The total area of the four walls of the room is \(660 \, m^2\).
- The length \(l\) is twice the width \(b\) (i.e., \(l = 2b\)).
- The height \(h\) of the room is \(11 \, m\).

### Step 2: Write 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
Calculating \(2 \times 11\):
\[ 660 = 22(l + b) \]

### Step 4: Solve for \(l + b\)
Now, divide both sides by \(22\):
\[ l + b = \frac{660}{22} = 30 \]

### Step 5: 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 6: Solve for \(b\)
Now, divide both sides by \(3\):
\[ b = \frac{30}{3} = 10 \, m \]

### Step 7: Find \(l\)
Using \(l = 2b\):
\[ l = 2 \times 10 = 20 \, m \]

### Step 8: Calculate the area of the ceiling
The area of the ceiling is given by:
\[ \text{Area of ceiling} = l \times b \]
Substituting the values of \(l\) and \(b\):
\[ \text{Area of ceiling} = 20 \times 10 = 200 \, m^2 \]

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

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