Solution to the Problem: The answer is 40 feet, not 42 feet!
The shortest route is not down to the floor, across the room, and up.
The spider actually travels over five of the six surfaces in the room.
To solve this problem, "unfold" the room, making a drawing of the six
surfaces in the room. Then connect the spider and the fly by a
line segment, and solve for the length of the segment.
I have
shown two ways to make the drawing below.
The drawing on the left
results in 42 feet, but the drawing on the right yields the shortest
route of 40 feet.
Use the Pythagorean Theorem to solve for the distance between the spider
and the fly.
The lengths of the legs of the right triangle are 32'
and 24'.
Therefore, the hypotenuse would be 40 feet.
See the picture
below:
