Question

If the perimeter of a square is 8 cm, what is the length of the diagonal?

2 square root of 2

4 square root of 2

square root of 2/ 2

4 cm

Answer 1

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

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

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

Therefore, the length of the diagonal is \(2\sqrt{2}\) cm. The correct answer is **2 square root of 2**.