FInd the Unknown Dimension in the Polyhedron

Let's just look at one face of this cube.

(Since it is a cube, all the faces are the exact same.)

The edge length is labeled "s".

Since the diagonal forms the hypotenuse of a right triangle,

and both legs are "s",

we can use the Pythagorean theorem to find s.

s² + s² = 9²

2s² = 81

s² = 40.5

s = \(+\sqrt{40.5} \approx 6.364 \text{ feet}\)

where did u get the diagram dude? Thats awesome!

Woudld that be a website?

Hectictar has given the edge length if the diagonal is across one face of the cube ...DB as shown below.......however.......if the diagonal is considered to be AB....we have...

AB  =  √[3s^2]

9  = √[3s^2]      square both sides

81  =  3 s^2      divide both sides by 3

27  =  s^2         take the square root of both sides

3√3  ft   =  s  ≈  5.19  ft.

Well, thanks, but yeah, I did need the 3d answer with x,y,z distance :)