$(8$ points$)$

A rectangular sheet of $8\mathrm{.}5$ inch by $11$ inch paper is placed on a flat surface. One of the corners is placed on

the opposite longer edge, s shown in the figure, and held there as the paper is smoothed flat. The problem

is to make the length of the crease as small as possible. Call the length L$.($Show all Work$)$

$($i$)$ What value x minimizes L$^(2)?$

$($ii$)$ What is the minimum value of L $?$