Question

If the perimeter of a square is 8 cm
8

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

4 cm
4

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𝑚
4 cm
4

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𝑚

2√2 cm
2
2

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𝑚
2√2 cm
2
2

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𝑚

42–√ cm
4
2

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42–√ cm
4
2

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𝑚

22–√ cm
2
2

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𝑚
22–√ cm

Answer 1

To find the length of the diagonal of a square given its perimeter, 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 length of one side. Given that the perimeter is 8 cm:

\[
4s = 8 \implies s = \frac{8}{4} = 2 \text{ cm}
\]

2. **Calculate the diagonal**: The length of the diagonal \( d \) of a square can be calculated using the formula \( d = s\sqrt{2} \).

Substituting the side length \( s \):

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

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

So the correct response is:

**2√2 cm**.