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A square sheet of paper has area 6 cm^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.

 

 Aug 12, 2018
 #1
avatar+10085 
+2

A square sheet of paper has area 6 cm^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.

laugh

 Aug 12, 2018
 #2
avatar+98129 
+2

Just wan tto try this one myself....!!!

 

The triangle will be a45-45-90 right triangle

Call the length of its legs, x

So...the area of the black triangle is  (1/2) (product of the leg lengths)  = (1/2)x^2

 

We also have two  "white" rectangles  each with an area  of  x ( √6 - x  )  = 2x (√6 - x)

And we have a "white" square  with an area  of (√6 - x)^2

 

Since the areas are equal...we have that

 

(1/2)x^2  = 2x(√6 - x)  + (√6 - x)^2

(1/2)x^2  = 2√6x - 2x^2  + 6  - 2√6x + x^2

(1/2)x^2  = -x^2 + 6

(3/.2)x^2  - 6   = 0

3x^2 - 12  = 0

3x^2  = 12

x^2  = 4

x =2

 

So...when  A  is folded over.....it will  be √ [ 2^2 + 2^2 ] = √8  =  2√2 cm  from it's original position

 

 

cool cool cool

 Aug 13, 2018

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