To find the length of the diagonal of a square using the Pythagorean Theorem, you can use the formula:
\[ d = s\sqrt{2} \]
where \( d \) is the length of the diagonal and \( s \) is the length of a side of the square.
Since the side length is not provided in your question, let's assume you are working with a square where the side length is \( s = 4 \) (as indicated in one of the responses), thus:
\[ d = 4\sqrt{2} \]
Calculating this:
- Calculate \( \sqrt{2} \) (approximately 1.414).
- Multiply \( 4 \) by \( \sqrt{2} \):
\[ d \approx 4 \times 1.414 \approx 5.656 \]
Rounding to the nearest hundredth:
\[ d \approx 5.66 \]
However, it's important to clarify which side length to work with, but if we use 4 for the side of the square, then the diagonal is approximately 5.66, not matching the options you provided.
If the side length was \( 2 \):
\[ d = 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \]
Which rounds to:
\[ d \approx 2.83 \]
Thus, based on the choices you've provided, if the side length of the square were 2, the correct answer is 2.83.
3 answers