If we connect points A and D with a line segment and we connect points B and C with a line
segment, then we will have a rectangle.
Side AB of rectangle ABCD is an edge of the cube. Since all edges of a cube have the same
length, we can pick a number for the length of the edge of the cube. Let’s let the length of an
edge of the cube be 1. So AB = 1. Diagonal AC of rectangle ABCD connects opposite vertices A
and C of the cube. Now in any rectangular solid having a length ℓ, a width w, and a height h,
the formula for the distance d between opposite vertices is given by the formula
. Here we have a cube, which is a rectangular solid where the length,
width, and height are all equal. Since we are letting the edge of the cube be 1, we have that
the length, width, and height are all equal to 1. So the length of AC is equal to