To find the length of the diagonal of a square, we can use the Pythagorean Theorem. If the side length of the square is \( s \), the diagonal \( d \) can be calculated using the formula:
\[ d = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2} \]
Now, let's calculate the diagonal for different side lengths to find the one that matches the options given (4.24, 8, 4, 2.83).
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If the side length \( s = 4 \): \[ d = 4\sqrt{2} \approx 4 \times 1.414 \approx 5.656 \]
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If the side length \( s = 2 \): \[ d = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828 \quad (\text{rounded to } 2.83) \]
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If the side length \( s = 8 \): \[ d = 8\sqrt{2} \approx 8 \times 1.414 \approx 11.312 \]
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If the side length \( s \approx 3 \): \[ d = 3\sqrt{2} \approx 3 \times 1.414 \approx 4.243 \quad (\text{rounded to } 4.24) \]
From the calculations, we see that:
- The diagonal for a square with side 2 is approximately 2.83.
- The diagonal for a square with side 3 is approximately 4.24.
The possible answers include 2.83 and 4.24.
If you need the most common side lengths in response to the problem statements or some specific context, please confirm or let me know if there's another specific side length to calculate.