A room `4m xx 12m` is to be carpeted by carpet 2m wide. What is the length of carpet?

Options

A. 12m
B. 30m
C. 24m
D. 48m

Answer

To solve the problem of determining the length of carpet needed to cover a room that measures 4 meters by 12 meters using a carpet that is 2 meters wide, we can follow these steps:

### Step 1: Calculate the Area of the Room
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

For the given room:
- Length = 12 meters
- Width = 4 meters

So, the area of the room is:
\[ \text{Area} = 12 \, \text{m} \times 4 \, \text{m} = 48 \, \text{m}^2 \]

### Step 2: Understand the Area Covered by the Carpet
The carpet is 2 meters wide. If we denote the length of the carpet as \( L \), the area covered by the carpet can be calculated as:
\[ \text{Area of Carpet} = \text{Width of Carpet} \times \text{Length of Carpet} \]
\[ \text{Area of Carpet} = 2 \, \text{m} \times L \]

### Step 3: Set the Area of the Carpet Equal to the Area of the Room
To find the length of the carpet needed, we set the area of the carpet equal to the area of the room:
\[ 2 \, \text{m} \times L = 48 \, \text{m}^2 \]

### Step 4: Solve for the Length of the Carpet
Now, we can solve for \( L \):
\[ L = \frac{48 \, \text{m}^2}{2 \, \text{m}} \]
\[ L = 24 \, \text{m} \]

### Final Answer
The length of the carpet needed to cover the room is **24 meters**.

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