Find the unknown dimension in the polyhedron: the edge length of a cube w/a diagonal of 9 ft. Please include a formula.
For a cube the length of the diagonal is given by sqrt(s^2 + s^2 + s^2), where s is the length of the edge.
Or length of the diagonal = sqrt (3*s^2)
Here the length of the diagonal is 9 ft.
=> 9 = sqrt (3*s^2)
=> 81 = 3*s^2
=> 81/3 = s^2
=> s = sqrt (81/3)
=> s = 9/sqrt 3
=> s = 3*sqrt 3
The edge length is 3*sqrt 3 ft.
The diagonal of a prism is given by "
D = sqrt( L^2 + W^2 + h^2)
But in the cube L =W+h
==> D = sqrt ( 3*L^2)
==> D = L*sqrt3............(1)
Now we need to find the length of the side is D= 9
==> 9 = L*sqrt3
==> L = 9/sqrt3 = 9sqrt3/3 = 3sqrt3.
Then the length of the side of the cube is 3*sqrt3.