Question

If the perimeter of a square is 8 cm
8

𝑐
𝑚
, what is the length of the diagonal?(1 point)
Responses

2√2 cm
2
2

𝑐
𝑚
2√2 cm
2
2

𝑐
𝑚

4 cm
4

𝑐
𝑚
4 cm
4

𝑐
𝑚

22–√ cm
2
2

𝑐
𝑚
22–√ cm
2
2

𝑐
𝑚

42–√ cm
4
2

𝑐
𝑚
42–√ cm

Answer 1

To find the length of the diagonal of a square, we first need to determine the side length of the square based on the given perimeter.

The formula for the perimeter \( P \) of a square is given by:

\[
P = 4s
\]

where \( s \) is the length of a side of the square. Given that the perimeter is 8 cm, we can solve for \( s \):

\[
4s = 8
\]

Dividing both sides by 4, we find:

\[
s = 2 \text{ cm}
\]

Next, we can find the length of the diagonal \( d \) using the formula:

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

Substituting \( s = 2 \) cm into the formula for the diagonal:

\[
d = 2 \sqrt{2} \text{ cm}
\]

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

The correct response is:

**2√2 cm**