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 8 8 4 4 4.24 4.24 2.83

Answer 1

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse \( c \) is equal to the sum of the squares of the lengths of the other two sides \( a \) and \( b \):

\[
c^2 = a^2 + b^2
\]

For a square with side length \( s \), both \( a \) and \( b \) are equal to \( s \). Thus, the diagonal \( d \) of the square can be calculated as follows:

\[
d^2 = s^2 + s^2 = 2s^2
\]

Taking the square root of both sides gives us:

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

If we take \( s = 4 \) (assuming this is the side length of the square from the options provided), the diagonal would be:

\[
d = 4\sqrt{2} \approx 4 \times 1.4142 = 5.6568
\]

Now, rounding to the nearest hundredth:

\[
d \approx 5.66
\]

However, if we are simply responding based on the given options without a specific side length provided, we look at the anticipated results: 8, 4, 4.24, 2.83.

If you are looking for a general answer, the closest option to the actual diagonal calculations for a square is not present. If \( s = 4 \), then these specific results lead to:

- No correct answer in the original options, since 5.66 isn’t listed.

However, confirming with the smallest side length of 2 (which gives \( d \approx 2.83 \)) fits among the options. Thus:

If negligible information about side length isn’t available, the closest value representing a diagonal calculation we find plausible is:

\[
\boxed{2.83}
\]