A square HSS $1271276\mathrm{.}4($G$40\mathrm{.}20/21)$ tension member is connected with $4$ lines of $90mm$ long fillet weld to a single $12mm$ plate welded into the slots of HSS walls as shown. The slot width is $14mm,$ and the end of the slot is not welded. Both the HSS and the plate are Grade $350W$ steel. The plate is bolted to the building frame with $6-$M$22$ bolts. Assume weld and bolt are adequate. Do not use section properties of ASTM A$500$ HSS$.$

a$)$ Calculate the factored tension resistance of the HSS with the weld length provided. Assume the plate does not govern the capacity.

b$)$ Calculate the minimum width $($W$)$ required for the $12mm$ plate to carry a factored tension load of $500kN.$ The minimum edge distance $($a$)$ is $38mm.[$ a $38mm].$ Assume block shear failure and the welded part of the plate do not govern the factored tension resistance of the plate. Round up the width to the nearest $5$ and $10.$