Geometry Problem - cubes?

Question

How would you determine the answer for this problem:

If a diagonal of a cube is 5 times the square root of three inches long, how long is an edge of the cube?

Thanks in advance!

Answer 1

abc ..
consider the "unit-cube" ... each side = 1
each "face-diagonal" = sqrt(1^2 + 1^2) = sqrt(1 + 1) =sqrt(2)

now the cube-diagonal is formed by the right-triangle whose sides are:
i) cube-side = 1
ii) face-diagonal = sqrt(2)

cube-diag = sqrt(1^2 + sqrt(2)^2) = sqrt(1 + 2) = sqrt(3)

consider: linear-dimensions have the same multiplier

(cube-side) / (cube-diag) = 1 / sqrt(3) = x / (5*sqrt(3))
x = (5*sqrt(3)) / sqrt(3) = 5

x = 5

the cube-side in question is the "edge of the cube" = 5 inches

Answer 2

Pythagorean Theorem, If you draw the diagonal of a side and the diagonal of the cube, you can see

that diagonal of the cube = sqrt(s^2+s^2+s^2) = s root(3)

So the side length is 5

Answer 3

The diagonal of a cube is the hypothenuse of a right angle triangle with sides
a,a*sqrt2
so
a^+2a^= 75
a^2=25 and a =5 = edge of the cube

Answer 4

frustrating yet there is sixty 4 cubes. sixteen could be painted on 2 factors. im attempting to try this in my head. there fairly isnt a formula for this. the only cubes that have 2 factors blue are those on the perimeters yet no longer the corners.