Answer:
~8.66cm
Step-by-step explanation:
The length of a diagonal of a rectangular of sides a and b is
[tex]\sqrt{a^2+b^2}[/tex]
in a cube, we can start by computing the diagonal of a rectangular side/wall containing A and then the diagonal of the rectangle formed by that diagonal and the edge leading to A. If the cube has sides a, b and c, we infer that the length is:
[tex]\sqrt{\sqrt{a^2+b^2}^2 + c^2} = \sqrt{a^2+b^2+c^2}[/tex]
Using this reasoning, we can prove that in a n-dimensional space, the length of the longest diagonal of a hypercube of edge lengths [tex]a_1, a_2, a_3, \ldots, a_n[/tex] is
[tex]\sqrt{a_1^2 + a_2^2 + a_3^2 + \ldots + a_n^2}[/tex]
So the solution here is
[tex]\sqrt{(5cm)^2 + (5cm)^2 + (5cm)^2} = \sqrt{75cm^2} = 5\sqrt{3cm^2} \approx 5\cdot 1.732cm = 8.66cm[/tex]
