A square piece of paper ABCD is black on one side and white on the other side and has an area of 3 in^2.

Corner A is folded over to point E which lies on the diagonal AC such that the total visible area is half black and half white.

So you're starting with this:

Code: Select all

```
B*---------*C
| / |
| / |
| / |
| / |
A*---------*D
```

And you're folding to get this;

Code: Select all

```
B*---------*C
| E / |
|____*/ |
\ | |
\ | |
-----*D
```

(Please let me know if this isn't right.)

How far is E from the fold line?

If the areas are equal then you have to find the area of the fold-over triangle so it matches the left-over of the square. Label the ends of the fold lines so we can describe things easier:

Code: Select all

```
B*---------*C
| E / |
|____*/ |
M \ | |
\ | |
N-----*D
```

Unfold this to see this:

Code: Select all

```
B*---------*C
| E / |
|____*/ |
M|\ | |
| \ | |
A*---N-----*D
```

MEN = BCDNEM and MEN = MAN. The area of the first square is BCDNEM + MEN + MAN = 3*MAN = 3 sq in. MAN is 45-45-90 triangle so it has the ratios they show

here. The area is (1/2)(AN)(AM) = 3 = (1/2)(b)(h). But b = h so 3 = (1/2)(h^2). So what is h? The fold line is MN. E is half this length because MN = AE and MANE is a square. So what is this distance?

Please write back if you get stuck. Thanks.