There is a rectangular paper with width 'a' . One corner is held and folded so that the corner touches the opposite edge of the paper. What is the minimum length of the crease ?
The maximum length of the crease is length of the paper. By symmetry, the minimum length of the crease will be $\displaystyle L = \sqrt{a^2 + a^2}$.
I guess someone will want to prove this using calculus by first getting a general expression for the crease length as a function of the distance of the corner of the paper from the opposite corner ....