Solve Problem $4\mathrm{.}146-$ except change problem as noted below. $(8$ points$)$ Change the load $P$ to $100$ kips $($was $90$ kips$)$ and the max. compressive stress to $22$ksi $($was $18$ksi $).$

NOTE: To minimize the work required, the moments of inertia of the cross$-$section have been provided relative to the axes added to the figure in the engineering paper worksheets.

$4\mathrm{.}146$ Knowing that $P=90$kips, determine the largest distance a for which the maximum compressive stress does not exceed $18$ksi.