Question

If the perimeter of a square is 8 cm, what is the length of the diagonal?(1 point)Responses2√2 cmStart Fraction Start Root 2 End Root over 2 End Fraction cm22–√ cm2 Start Root 2 End Root cm4 cm4 cm42–√ cm

Answer 1

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

1. **Calculate the side length of the square**:
The perimeter \( P \) of a square is given by the formula:
\[
P = 4s
\]
where \( s \) is the length of a side of the square. Given that the perimeter is 8 cm:
\[
8 = 4s
\]
Dividing both sides by 4 gives:
\[
s = 2 \, \text{cm}
\]

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

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