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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.

 

 May 7, 2021
 #1
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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     

 May 7, 2021
edited by ElectricPavlov  May 7, 2021
 #2
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Area of black and white square = 2/3(16)

 

2/3(16) = 10 2/3

 

Distance = sqrt(2 * 10 2/3)

 May 8, 2021

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