A rectangular sheet of paper is folded so that two diagonally opposite corners come together. The crease thus formed is as long as the longer side of the rectangle.
What is the ratio of the longer side of the rectangle to the shorter?
Hmmm... I'm not sure I am clear on what DJ is asking, but I think I understand it.
If so, we find that
Where:
x is the long side,
y is the short side, and
theta is the interior angle between the long side and the diagonal.
x * tan(theta) = y, and
x * sin (90-theta) = y
subtract one equation from the other:
x * ( tan(theta) - sin(90-theta) ) = 0
divide by x, and we see that this is independent of the lengths of x and y (as it should be):
tan(theta) - sin (90-theta) = 0
solving numerically, we find theta equals
0.666243 radians
This means that since y/x = tan (theta) = .786157,
y/x = .786157
and x/y = 1.27201
Solution - I think
