A ladybug is sitting in one corner of a cubic room with each side of length 10 feet. She wants to walk to the extreme opposite corner (the one farthest from her). What is the shortest path that she should take?
Solution: The shortest path is the one shown in the top image below where we have flattened out the sides of the room. The reason this is the shortest path is that a straight line is the shortest distance between two points on a plane and the path shown in dashed lines below is a straight line. It is the diagonal of a rectangle of sides 10 feet x 20 feet. By Pythagorus’s theorem, the length of this path will be (100+400)1/2= 22.36 feet. The way the bug will have to walk is shown in the bottom figure.
