Question

the diagonal of a square with sides 4 units is √32 units. which state BEST describes the diagonal?

A: it is between 5 and 6, but closer to 6 units.
B: it is between 4 and 5, but closer to 4 units.
C: it is between 5 and 6, but closer to 5 units.
Or D: it is between 4 and 5, but closer to 5 units.

Answer 1

To find the diagonal of a square, you can use the formula:

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

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

In this case, the side length \(s\) is 4 units:

\[
d = 4\sqrt{2}
\]

To approximate \(\sqrt{2}\), we know that it is approximately \(1.414\). Therefore:

\[
d \approx 4 \times 1.414 \approx 5.656
\]

Now, let's evaluate the options based on the calculation:

- The diagonal \(d \approx 5.656\), which is between 5 and 6.
- Since 5.656 is closer to 6 than to 5, the best choice is:

**A: it is between 5 and 6, but closer to 6 units.**