+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.
+12528 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.
+128566 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
