SH1 NJC Revision Package Vol 2 Q3

A rectangular piece of paper is \(24\) cm long and \(12\) cm wide. The upper right-hand corner is folded down to reach the bottom edge of the paper at \(C\) as shown below.

Show that \(\vartriangle APC\) and \(\vartriangle CQB\) are similar triangles and hence show that \(x=\frac{\sqrt{6}y}{\sqrt{y-6}}\).[4]

By using differentiation, find the minimum length of the resulting crease \(AB\).[5]