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 2.83 2.83 8 8 4 4 4.24 4.24

Answer 1

The Pythagorean Theorem states that for a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In the case of a square, the diagonal forms a right triangle with two sides of the square.

If each side of the square has length \( s \), 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 a square with side length \( s = 4 \):

\[
d = 4\sqrt{2} \approx 4 \times 1.414 \approx 5.656
\]

Rounding 5.656 to the nearest hundredth gives us 5.66.

Now, for the options provided: 2.83, 8, 4, and 4.24, it seems like the best answer for \( s = 4 \) may not directly match with the diagonal calculation.

Let's check with another side length of \( s = 2 \):

\[
d = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828
\]

Rounding 2.828 gives us 2.83, which matches one of the provided options.

Thus, if the side length of the square is 2, the length of the diagonal rounded to the nearest hundredth is:

**2.83**