If the length and the breadth of a rectangle are doubled then its area

Options

A. remains same
B. becomes half
C. doubles
D. becomes four times

Answer

To solve the problem of how the area of a rectangle changes when both its length and breadth are doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Original Dimensions**:
Let the original length of the rectangle be \( l \) and the original breadth be \( b \).

2. **Calculate the Original Area**:
The area \( A_1 \) of the rectangle can be calculated using the formula:
\[ A_1 = l \times b \]

3. **Double the Dimensions**:
When the length and breadth are doubled, the new length becomes \( 2l \) and the new breadth becomes \( 2b \).

4. **Calculate the New Area**:
The area \( A_2 \) of the new rectangle can be calculated as:
\[ A_2 = (2l) \times (2b) = 4lb \]

5. **Compare the Areas**:
Now, we can compare the new area \( A_2 \) with the original area \( A_1 \):
\[ A_2 = 4 \times A_1 \]
This means that the new area is four times the original area.

### Conclusion:
Thus, if the length and breadth of a rectangle are doubled, the area becomes **four times** the original area.

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