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?

Let a be the short side and b the longer. Then the triangle formed by a, b and the diagonal is similar to that formed by b, half the diagonal, and half the crease. So we have:

a/b = (1/2b)/(√(a^2 + b^2))

which gives a = b * √((√5 - 1)/2)

or

b = a * √(2/(√5 - 1))

Posted by RoyCook on 2003-09-24 10:43:15