Question

Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary. (1 point) Responses 4.24 4.24 8 8 2.83 2.83 4

Answer 1

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:

1. Calculate \( \sqrt{2} \) (approximately 1.414).
2. 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**.