The perimeter of two squares is 12 cm and 24 cm. The area of the bigger square is how many times that of the smaller?

Options

A. 2 times
B. 3 times
C. 4 times
D. 5 times

Answer

To solve the problem, we need to find the area of two squares based on their given perimeters and then determine how many times the area of the larger square is compared to the smaller square.

### Step-by-Step Solution:

1. **Identify the Perimeters**:
- The perimeter of the first square (P1) is 12 cm.
- The perimeter of the second square (P2) is 24 cm.

2. **Find the Side Lengths of the Squares**:
- The formula for the perimeter of a square is given by:
\[ P = 4 \times \text{side} \]
- For the first square:
\[ 4 \times a = 12 \implies a = \frac{12}{4} = 3 \text{ cm} \]
- For the second square:
\[ 4 \times b = 24 \implies b = \frac{24}{4} = 6 \text{ cm} \]

3. **Calculate the Areas of the Squares**:
- The area of a square is calculated using the formula:
\[ \text{Area} = \text{side}^2 \]
- For the first square:
\[ \text{Area}_1 = a^2 = 3^2 = 9 \text{ cm}^2 \]
- For the second square:
\[ \text{Area}_2 = b^2 = 6^2 = 36 \text{ cm}^2 \]

4. **Determine How Many Times the Area of the Bigger Square is Compared to the Smaller Square**:
- We need to find the ratio of the area of the second square to the area of the first square:
\[ \text{Ratio} = \frac{\text{Area}_2}{\text{Area}_1} = \frac{36 \text{ cm}^2}{9 \text{ cm}^2} = 4 \]

5. **Conclusion**:
- The area of the bigger square is 4 times that of the smaller square.

### Final Answer:
The area of the bigger square is 4 times that of the smaller square.

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