I just added the diagram. I couldn't make it on this form.
The Problem: A rectangular piece of paper, ABCD, is folded so that point B lies on point D. It is then unfolded to show the crease XY. If AX = 6 and XB = 10, find the length of the crease XY.
10 X 6
B________________________ A
| / |
| / |
| / |
| ________/______________ |
C Y D
I realize that both AB and CD are 16 across. I've tried turning parts of this rectangel into a triangle. But that didn't yield results, as I couldn't determine the new figure's length. The closest I got to a lead was My thought of drawing a line from Y to A. That would give me a triangle with a base of 6, but no angles, so no way to determine XY.
Since you have a rectangle, the length is half the width. So and are 8.
And you can make this picture: link
Now apply the Pythagorean Theorem a bunch of times.
Then apply it again:
Now let's fill that in our pic: link
Since is an angle bisector, then
So both are 8.
Apply Pythagorean Theorem to get
And without more info, I don't see how you can find
I don't have time to get to it right now, but I'll try (no promises) to get back to it later.
Note that whereas we don't know the width of the rectangle, we do know that points B and D lie the same distance away from the fold along the red line (the diagonal) because when the paper is folded these points overlap. My diagram stinks, but it gives you the idea behind what I'm talking about anyway.
Edit: Oh! I almost forgot. BD and XY have to be perpendicular as well. Do you see why that is?
-Dan