What is the perimeter of a square with a diagonal measuring eight times the square root of two centimeters?

To find the perimeter of a square when its diagonal is known, it is helpful to remember the relationship between the diagonal and the side length of the square. For a square, the diagonal can be expressed using the equation:

[ d = s\sqrt{2} ]

where ( d ) is the diagonal and ( s ) is the side length of the square. Here, the diagonal is given as ( 8\sqrt{2} ) centimeters, so we can set this equal to the diagonal formula:

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

To isolate ( s ), divide both sides by ( \sqrt{2} ):

[ s = 8 ]

Now that we have the side length of the square, we can calculate the perimeter. The perimeter ( P ) of a square is given by the formula:

[ P = 4s ]

Substituting in the value of ( s ):

[ P = 4 \times 8 = 32 ]

Therefore, the perimeter of the square is 32 centimeters, which corresponds to the correct choice.