The length of square \( A \) is twice the length of the side of square \( B \). What is the ratio between the area of square \( A \) and square \( B \) ?

To determine the ratio between the areas of square \( A \) and square \( B \), let's follow these steps: 1. **Define the Side Lengths:** - Let the side length of square \( B \) be \( s \). - According to the problem, the side length of square \( A \) is twice that of square \( B \). Therefore, the side length of square \( A \) is \( 2s \). 2. **Calculate the Areas:** - **Area of Square \( B \):** \[ \text{Area}_B = s \times s = s^2 \] - **Area of Square \( A \):** \[ \text{Area}_A = (2s) \times (2s) = 4s^2 \] 3. **Determine the Ratio of Areas:** - The ratio of the area of square \( A \) to the area of square \( B \) is: \[ \frac{\text{Area}_A}{\text{Area}_B} = \frac{4s^2}{s^2} = 4 \] - This simplifies to a ratio of \( 4:1 \). **Conclusion:** The area of square \( A \) is **4 to 1** compared to the area of square \( B \).