How many metres of carpet 63 cm wide will be required to cover the floor of a room 14 m by 9m

Options

A. 200m
B. 210m
C. 220m
D. 185m

Answer

To find out how many meters of carpet 63 cm wide will be required to cover the floor of a room that measures 14 m by 9 m, we can follow these steps:

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

Given:
- Length of the room = 14 m
- Breadth of the room = 9 m

So, the area of the room is:
\[ \text{Area} = 14 \, \text{m} \times 9 \, \text{m} = 126 \, \text{m}^2 \]

### Step 2: Convert the width of the carpet from cm to m
The width of the carpet is given as 63 cm. We need to convert this measurement into meters:
\[ 1 \, \text{cm} = \frac{1}{100} \, \text{m} \]

Thus,
\[ 63 \, \text{cm} = \frac{63}{100} \, \text{m} = 0.63 \, \text{m} \]

### Step 3: Calculate the length of the carpet required
The area of the carpet that will cover the room must equal the area of the room. The area of the carpet can also be calculated using the formula:
\[ \text{Area of carpet} = \text{Length of carpet} \times \text{Width of carpet} \]

Let \( L \) be the length of the carpet required. Therefore:
\[ \text{Area of carpet} = L \times 0.63 \]

Setting the area of the carpet equal to the area of the room:
\[ L \times 0.63 = 126 \]

To find \( L \), we rearrange the equation:
\[ L = \frac{126}{0.63} \]

### Step 4: Perform the division
To simplify the division, we can eliminate the decimal by multiplying both the numerator and the denominator by 100:
\[ L = \frac{126 \times 100}{63} \]
\[ L = \frac{12600}{63} \]

Now, we can simplify:
\[ L = 200 \, \text{m} \]

### Conclusion
The required length of the carpet is **200 meters**.

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