The area of four walls of a room is `120 m^(2)` . If the length of the room is twice its breadth and the height is 4 m, find the area of the floor.

Answer

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

### Step 1: Understand the given information
We know:
- The area of the four walls of the room = 120 m²
- The height of the room = 4 m
- The length of the room is twice its breadth.

### Step 2: Define variables
Let:
- The breadth of the room = \( x \) meters
- The length of the room = \( 2x \) meters (since the length is twice the breadth)

### Step 3: 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:
\[ \text{Area of four walls} = 2 \times (l + b) \times h \]
Substituting the values we have:
\[ 120 = 2 \times (2x + x) \times 4 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 120 = 2 \times (3x) \times 4 \]
\[ 120 = 24x \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 24:
\[ x = \frac{120}{24} = 5 \text{ meters} \]

### Step 6: Find the length of the room
Now that we have \( x \), we can find the length:
\[ \text{Length} = 2x = 2 \times 5 = 10 \text{ meters} \]

### Step 7: Find the area of the floor
The area of the floor (which is a rectangle) is given by:
\[ \text{Area of floor} = \text{Length} \times \text{Breadth} \]
Substituting the values we found:
\[ \text{Area of floor} = 10 \times 5 = 50 \text{ m}^2 \]

### Final Answer
The area of the floor is \( 50 \, \text{m}^2 \).

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