What is the new perimeter of a square whose side has been halved?

Answer

To find the new perimeter of a square whose side has been halved, follow these steps:

### Step 1: Understand the formula for the perimeter of a square.
The perimeter (P) of a square is calculated using the formula:
\[ P = 4 \times \text{side} \]
Let’s denote the original side of the square as \( a \).

### Step 2: Calculate the original perimeter.
Using the formula:
\[ P_{\text{original}} = 4 \times a \]
This gives us the original perimeter of the square.

### Step 3: Determine the new side length after halving.
If the side of the square is halved, the new side length becomes:
\[ \text{new side} = \frac{a}{2} \]

### Step 4: Calculate the new perimeter using the new side length.
Now, substitute the new side length into the perimeter formula:
\[ P_{\text{new}} = 4 \times \left(\frac{a}{2}\right) \]
This simplifies to:
\[ P_{\text{new}} = 4 \times \frac{a}{2} = 2a \]

### Step 5: Compare the new perimeter with the original perimeter.
From our calculations:
- The original perimeter was \( 4a \).
- The new perimeter is \( 2a \).

### Conclusion:
The new perimeter of the square, after halving the side length, is:
\[ P_{\text{new}} = 2a \]
This shows that the new perimeter is half of the original perimeter.

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