Question
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 \( B \) ?
Ask by Stewart Pritchard. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The area of square \( A \) is 4 times the area of square \( B \), so the ratio is 4:1.
Solution
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 \( B \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
The area of a square is calculated by squaring the length of its side. If the side length of square \( B \) is \( s \), then the length of square \( A \) would be \( 2s \). Therefore, the area of square \( A \) is \( (2s)^2 = 4s^2 \), and the area of square \( B \) is \( s^2 \). Now, to find the ratio of the areas, we take the area of square \( A \) and divide it by the area of square \( B \): \[ \text{Ratio} = \frac{\text{Area of } A}{\text{Area of } B} = \frac{4s^2}{s^2} = 4. \] Thus, the ratio of the area of square \( A \) to square \( B \) is \( 4:1 \).
