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

Options

A. tripled
B. doubled
C. made half
D. none of these

Answer

To solve the problem, we need to determine how the perimeter of a rectangle changes when both its length and breadth are doubled. Let's break this down step by step.

### Step-by-Step Solution:

1. **Understand the formula for the perimeter of a rectangle**:
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (L + B) \]
where \(L\) is the length and \(B\) is the breadth of the rectangle.

2. **Identify the new dimensions**:
If the length and breadth are doubled, the new length \(L'\) and new breadth \(B'\) can be expressed as:
\[ L' = 2L \quad \text{and} \quad B' = 2B \]

3. **Calculate the new perimeter**:
Substitute the new dimensions into the perimeter formula:
\[ P' = 2 \times (L' + B') = 2 \times (2L + 2B) \]

4. **Simplify the expression**:
Factor out the common term:
\[ P' = 2 \times (2(L + B)) = 4 \times (L + B) \]

5. **Relate the new perimeter to the old perimeter**:
Recall the original perimeter:
\[ P = 2 \times (L + B) \]
Now, we can express the new perimeter in terms of the old perimeter:
\[ P' = 4 \times (L + B) = 2 \times (2 \times (L + B)) = 2 \times P \]

6. **Conclusion**:
Therefore, when the length and breadth of a rectangle are doubled, the new perimeter is:
\[ P' = 2P \]
This means the new perimeter is double the original perimeter.

### Final Answer:
The perimeter is **double**.

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