A square's diagonal has a length equal to √(2) times the length of its sides. So if the side length is x, then the diagonal is such that
√(2) x = 10 cm
→ x = 10/√(2) cm ≈ 7.07 cm
The perimeter of a square is 4 times its side length, so the perimeter is
4 (10/√(2) cm) = 40/√(2) cm ≈ 28.3 cm
which makes 28.4 cm the closest answer.
