d0mine on Interesting math puzzle - harder than it sounds

for the unraveled room:

  sqrt(1+x^2) + sqrt((6-x)^2+y^2)+sqrt(12^2+z^2)+
  sqrt((30-z-y)^2+u^2)+sqrt((6-u)^2+1)

  40 at {x -> 0.75, y -> 7, z -> 16, u -> 5.25}

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