Question

The diagonal of a square with sides 4 units is v32 units. Which state best describes the diagonal?




The diagonal of a square with sides 4 units is units. Which state best describes the diagonal?




It is between 4 and 5, but closer to 4units.


It is between 5 and 6, but closer to 5 units.


It is between 4 and 5, but closer to 5 units.


It is between 5 and 6, but closer to 6 units.

Answer 1

To find the length of 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.

Given that the side length \( s = 4 \) units, the diagonal is calculated as:

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

Now, we can approximate \( \sqrt{2} \approx 1.414 \):

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

Thus, the diagonal is approximately 5.656 units.

Now, looking at the options provided:

- It is between 4 and 5, but closer to 4 units.
- It is between 5 and 6, but closer to 5 units.
- It is between 4 and 5, but closer to 5 units.
- It is between 5 and 6, but closer to 6 units.

Since 5.656 is between 5 and 6, but closer to 6, the best description of the diagonal is:

**It is between 5 and 6, but closer to 6 units.**