The midpoints of the adjacent sides of a square are connected to form a new square. What is the number of inches in the perimeter of the original square if the perimeter of the new square is 16 inches? Express your answer in simplest radical form.
The side length, S, of the original square can be found as
16 = sqrt ( 2 * S^2/4)
256 = S^2 / 2
512 = S^2
S = sqrt (512) = 16sqrt (2)
The perimeter of the original square= 4 * 16sqrt (2) = 64sqrt (2)