# Find the unknown dimension in the polyhedron: the edge length of a cube w/a diagonal of 9 ft. Please include a formula. 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

==>...

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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.

Approved by eNotes Editorial Team 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.

Approved by eNotes Editorial Team