+0  
 
0
70
2
avatar+45 

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.

 

anomy  Aug 12, 2018
 #1
avatar+9552 
+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

Omi67  Aug 12, 2018
 #2
avatar+88899 
+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

CPhill  Aug 13, 2018

11 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.