The side of a square is 10cm. How many times will the new perimeter become if the side of the square is doubled?

Options

A. 2 times
B. 4 times
C. 6 times
D. 8 times

Answer

To solve the problem step by step, we will calculate the perimeter of the square with the given side length and then determine how many times the perimeter increases when the side is doubled.

### Step 1: Calculate the perimeter of the original square.
The formula for the perimeter (P) of a square is:
\[ P = 4 \times \text{side} \]

Given that the side of the square is 10 cm:
\[ P = 4 \times 10 \]
\[ P = 40 \text{ cm} \]

### Step 2: Determine the new side length after doubling.
If the side of the square is doubled, the new side length will be:
\[ \text{New side} = 10 \times 2 = 20 \text{ cm} \]

### Step 3: Calculate the perimeter of the new square.
Using the same formula for the perimeter:
\[ P = 4 \times \text{new side} \]
\[ P = 4 \times 20 \]
\[ P = 80 \text{ cm} \]

### Step 4: Compare the new perimeter with the original perimeter.
Now we need to find out how many times the new perimeter is compared to the old perimeter:
- Old perimeter = 40 cm
- New perimeter = 80 cm

To find how many times the new perimeter is compared to the old perimeter, we divide the new perimeter by the old perimeter:
\[ \text{Times} = \frac{\text{New perimeter}}{\text{Old perimeter}} \]
\[ \text{Times} = \frac{80}{40} = 2 \]

### Conclusion:
The new perimeter is 2 times the old perimeter.