To find the length of the diagonal of a square when the perimeter is given, we can follow these steps:
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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 \(s\): \[ 4s = 8 \implies s = \frac{8}{4} = 2 \text{ cm} \]
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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.
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