A square sheet of paper has area 16cm^2 The front is white and the back is black. When the sheet is folded so that point A rests on the diagonal as shown, the visible black area is equal to the visible white area. How many centimeters is A from its original position? Express your answer in simplest radical form.
+36916 The dotted line triangle + Visible black area + visible white area = 16 cm^2 so each is 16/3 cm^2
Square with area 16/3
has sides x^2 = 16/3
x = 4 /sqrt3
diagonal = sqrt ( (4 /sqrt3)^2 + (4/ sqrt3)^2 )
= sqrt (32/3)
A has moved 4 sqrt (2/3) =4/3 * sqrt 6
