Question 69
The tiny, but extremely precious, Dodecahedral Diamond lies 2 meters from the south wall and 3 meters from the west wall of a rectangular room whose north and south walls are 4 meters long and whose east and west walls are 3 meters long. A thief lowers himself from the ceiling into the room and touches the floor one meter from the south wall and one meter from the west wall. However, he realizes that he must immediately deactivate the alarm system, by cutting in at least one point a wire that runs at a constant height from the ground along the four perimeter walls of the room. How many meters long is the shortest path he must take to reach first any point of one of the walls, and then the Dodecahedral Diamond?
(A) $3+\sqrt{2}$
(B) $2+\sqrt{5}$
(C) $\sqrt{17}$
(D) $\sqrt{13}$
(E) $2 \sqrt{2}$.
(A) $3+\sqrt{2}$
(B) $2+\sqrt{5}$
(C) $\sqrt{17}$
(D) $\sqrt{13}$
(E) $2 \sqrt{2}$.