If each sides of a triangle is doubled then how many times the perimeter of triangle increased?

Answer

To solve the problem of how many times the perimeter of a triangle increases when each side is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Define the sides of the triangle**: Let the sides of the triangle be denoted as \( A \), \( B \), and \( C \).

2. **Calculate the original perimeter**: The perimeter \( P \) of the triangle can be calculated using the formula:
\[ P = A + B + C \]

3. **Double the sides**: When each side of the triangle is doubled, the new sides become:
\[ 2A, \quad 2B, \quad 2C \]

4. **Calculate the new perimeter**: The new perimeter \( P' \) can be calculated as:
\[ P' = 2A + 2B + 2C \]

5. **Factor out the common factor**: We can factor out the 2 from the new perimeter:
\[ P' = 2(A + B + C) \]

6. **Relate the new perimeter to the old perimeter**: Since \( A + B + C \) is the original perimeter \( P \), we can substitute:
\[ P' = 2P \]

7. **Conclusion**: This means that the new perimeter is twice the original perimeter. Therefore, the perimeter of the triangle increases by a factor of 2.

### Final Answer:
The perimeter of the triangle increases by **2 times**.

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