The diagonal of a cube is the square root of 3x^2, where x is a side length....The three dimensional diagonal is the counterpart to the two dimensional hypotenuse found in a right triangle...mathematically a three dimension diagonal can be found with an extension of the Pythagorean Theorem adapted to three dimensions...
d^2=x^2+y^2+z^2 but since we are dealing with a cube, x=y=z=s where s is a side lenght...
d^2=3s^2 and we are told that the diagonal is 30 in. so
3s^2=30^2
3s^2=900
s^2=300
s=√300
s=10√3 in. exact
s≈17.3 in. (to the nearest tenth of an inch)
