(pythagorean theorem)
a diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube. find the length to a diagonal d in a cube that has an edge of length 10 meters.

First draw a picture (see attached).

You want to find the diagonal of the cube, length AB.
The right triangle formed is trianagle ABD.
AD = 10m

DB will be the hypotenuse of triangle BCD.
.

If we know the length of AD and DB, we can find AB.


In fact, the diagonal of any cube is √3 times the side length of the cube.
Let s be the side length (as in AD or CD in the attached) and
h be the hypotenuse of the base, (DB in the attached) and
d be the diagonal of the cube (AB in the attached).

The hypotenuse of the base will be:.

The cube's diagonal will be:
.

Substituting  as , you have