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**+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.

Omi67
Aug 12, 2018

#2**+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

CPhill
Aug 13, 2018