Question

If the perimeter of a square is 8 cm
8

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

22–√ cm
2
2

𝑐
𝑚
22–√ cm
2
2

𝑐
𝑚

42–√ cm
4
2

𝑐
𝑚
42–√ cm
4
2

𝑐
𝑚

4 cm
4

𝑐
𝑚
4 cm
4

𝑐
𝑚

2√2 cm

Answer 1

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

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

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

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

**Final answer: \(2\sqrt{2} \text{ cm}\)**.