PS$\mathrm{.}63$ An insurance claims processing company moves paperwork among four process steps. Each process step is performed in four separate areas. Each area is located on the same side of a corridor with a distance of $35$ feet between each area. We'll call this existing arrangement Layout $1.$

Layout $1$

$\backslash$table$[[,$larr$35ft,$Area C$,$larr$35ft,$Area D$],[,$larr Corridor $,,,]]$

In an effort to become more efficient, the company is looking to move two of these areas across the corridor. The distance across the corridor is $13$ feet and the distance between areas down the corridor is still $35$ feet. $($For example, going from A to B is $35$ feet; $C$ to $D$ is also $35$ feet. A to C is $13$ feet; B to D is also $13$ feet. And for the purposes of this problem, the distance from $A$ to $D$ is $37$ feet, as is the distance from $B$ to $C.)$ We'll call this proposed arrangement Layout $2.$

Layout $2$

$\backslash$table$[[$Area A$,$larr$\sqrt[\phantom{2}]{35}ft,$Area B$],[darr13$ftuarr,larr Corridor $,$darr$13$ftuarr