How do you find the length of a line from one corner of a cube to another?

Answer 1

Pythagorean theorem:

A^2 + B^2 = C^2 A squared plus B squared equals C squared

Two triangles will need to be solved: ABC and ACD.

For a cube, where A = B on any side, the hypotenuse C on any cube's surface would be the base of an internal triangle whose hypotenuse D would connect two opposing corners through the cube's center. Therefore, to solve for D:

D^2 = A^2 + C^2 where

C^2 = A^2 + B^2 Then by substitution:

D^2 = A^2 + A^2 + B^2 Then by reflexive:

D^2 = A^2 + A^2 + A^2 Then by distributive:

D^2 = 3A^2 And finally square rooting both sides of the equation:

D=sqrt(3A^2)

If A = 1, then

D = sqrt(3(1^2)

D = 1.732

JCS