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Answer:
P ≅ 62 cm
Step-by-step explanation:
The perimeter of a square of side length s is P = 4s. Given that the diagonal of this particular square has length 22 cm, we need to find the side length, s, as a preliminary to finding the perimeter, P, of the square.
The Pythagorean Theorem applies to the diagonal: the diagonal is the hypotenuse of the square. Recalling that s is the side length, and that the triangle formed by the diagonal is a right triangle with equal side lengths,
s^2 + s^2 = (22 cm)^2. Then 2s^2 = 484 cm^2, and s^2 = 242 cm^2.
The side length is thus s = +√(242 cm^2). This radical cannot be reduced to a more compact form.
Then the perimeter is P = 4s, or 4·√(242 cm^2). This comes out to approximately
P ≅ 62 cm