Question

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

42–√ cm
4 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

22–√ cm

Answer 1

To find the length of the diagonal of a square when the perimeter is given, we can first determine the length of one side of the square.

The perimeter \( P \) of a square is calculated using the formula:
\[
P = 4s
\]
where \( s \) is the length of a side.

Given that the perimeter is 8 cm:
\[
4s = 8 \implies s = \frac{8}{4} = 2 \text{ cm}
\]

Next, we use the formula for the diagonal \( d \) of the square, which is given by:
\[
d = s\sqrt{2}
\]
Substituting \( s = 2 \) cm into the formula:
\[
d = 2\sqrt{2} \text{ cm}
\]

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

So the correct response is:
\[
\text{2}\sqrt{2} \text{ cm}
\]