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)
4
2.83
8
4.24

Answer 1

To find the length of the diagonal of a square using the Pythagorean Theorem, you can use the formula:

\[
d = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2}
\]

where \( d \) is the diagonal length and \( s \) is the side length of the square.

Assuming the side length of the square \( s \) is 8 (from the options given), the calculation would be:

\[
d = 8\sqrt{2} \approx 8 \times 1.414 \approx 11.31
\]

Now, let's evaluate the options you provided:

1. 4
2. 2.83
3. 8
4. 4.24

None of these appear to be directly related to the diagonal of a square with a side length of 8. Let's check if they correspond to a different side length:

If the side length \( s = 4 \):

\[
d = 4\sqrt{2} \approx 4 \times 1.414 \approx 5.66
\]

If \( s = 2.83 \):

\[
d = 2.83 \sqrt{2} \approx 2.83 \times 1.414 \approx 4
\]

If \( s = 4.24 \):

\[
d = 4.24\sqrt{2} \approx 4.24 \times 1.414 \approx 6
\]

To summarize:

- The diagonal corresponding to \( s = 4 \) is approximately \( 5.66 \)
- The diagonal corresponding to \( s = 2.83 \) is approximately \( 4 \)
- The diagonal corresponding to \( s = 4.24 \) is approximately \( 6 \)

Thus, from the options you provided, none of them seem to be correct if we are assuming conventional square side lengths. However, if you meant the square's side length is \( 2 \) which results in a diagonal of approximately \( 2.83 \) (since \( d = 2\sqrt{2} \approx 2.83) \).

If you simply need to pick the closest answer for the diagonal of a unit square or a square with side length 2, the answer would be 2.83.

Otherwise, please clarify the specific side length of the square to find the correct diagonal based on the theorem.