Find the perimeter of a square with the diagonal 22cm.
perimeter =

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