Suppose you could climb to the top of the great pyramid of giza in egypt. which path would be shorter, climbing a lateral edge or the slant height? justify your response.

Check the picture below.

if you go from the slant height, the path is shorter to the top, since the hypotenuse is the longest of all sides in a right-triangle.

that said, is shorter but is also steeper, so the lateral edge is longer but less steep and thus a bit simpler though longer, but we're only asked on which is shorter.

Earth to neptune and the difference is 3 times greater

Yes because it is a different way of writing it, but it is the same numbers