The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?
The number \(x\) is such a number that exactly one of the four numbers \(a = x - \sqrt{2}\), \(b = x-1/x\), \(c = x + 1/x\), \(d = x^2 + 2\sqrt{2}\) is not an integer. Find all such \(x\).
Ben is going to bend a square sheet of paper \(ABCD\). Ben calls the fold beautiful, if the side \(AB\) crosses the side \(CD\) and the four resulting rectangular triangles are equal. Before that, Jack selects a random point on the sheet \(F\). Find the probability that Ben will be able to make a beautiful fold through the point \(F\).