Answer: 13.8 cm
Step-by-step explanation:
Assuming the cube is the cube shown in the attached image, its diagonal is [tex]x[/tex].
Now, for a cube which each side is [tex]a[/tex], its diagonal is given by the pithagorean theorem:
[tex]x=\sqrt{a^{2}+d^{2}}[/tex] (1)
Where [tex]d[/tex] is the hypothenuse of the right triangle formed in one of the cube's faces:
[tex]d=\sqrt{3}a[/tex] (2)
Then the formula for the diagonal is:
[tex]x=\sqrt{a^{2}+(\sqrt{3}a)^{2}}[/tex] (3)
[tex]x=\sqrt{3}a[/tex] (4)
If [tex]a=8 cm[/tex]:
[tex]x=\sqrt{3}8 cm[/tex] (5)
Finally:
x=13.8 cm
