Question

If the perimeter of a square is 8 cm, what is the length of the diagonal?(1 point)
Responses

22–√ cm
2 Start Root 2 End Root cm

2√2 cm
Start Fraction Start Root 2 End Root over 2 End Fraction cm

4 cm
4 cm

42–√ cm

Answer 1

To find the length of the diagonal of a square when the perimeter is given, we can follow these steps:

1. **Calculate the side length of the square**: The formula for the perimeter \(P\) of a square is given by:
\[
P = 4s
\]
where \(s\) is the side length. Given \(P = 8 \, \text{cm}\), we can solve for \(s\):
\[
8 = 4s \implies s = \frac{8}{4} = 2 \, \text{cm}
\]

2. **Calculate the diagonal**: The length \(d\) of the diagonal of a square can be calculated using the formula:
\[
d = s\sqrt{2}
\]
Substituting \(s = 2 \, \text{cm}\) into the formula gives:
\[
d = 2\sqrt{2} \, \text{cm}
\]

Therefore, the length of the diagonal is \(2\sqrt{2} \, \text{cm}\).

The correct response is \(2\sqrt{2} \, \text{cm}\).