Question

If the perimeter of a square is 8 cm, what is the length of the diagonal?
4cm
Sqrt2 over 2
4sqrt2
2sqrt2

Answer 1

The perimeter of a square is given by the formula:

\[
P = 4s
\]

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

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

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

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

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

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

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

Thus, the correct answer is \(2\sqrt{2}\).