Question

The diagram shows a 5 cm x 5 cm x 5 cm cube.

Answer 1

Answer:

~8.66cm

Step-by-step explanation:

The length of a diagonal of a rectangular of sides a and b is

$\sqrt{a^2+b^2}$

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:

$\sqrt{\sqrt{a^2+b^2}^2 + c^2} = \sqrt{a^2+b^2+c^2}$

Using this reasoning, we can prove that in a n-dimensional space, the length of the longest diagonal of a hypercube of edge lengths $a_1, a_2, a_3, \ldots, a_n$ is

$\sqrt{a_1^2 + a_2^2 + a_3^2 + \ldots + a_n^2}$

So the solution here is

$\sqrt{(5cm)^2 + (5cm)^2 + (5cm)^2} = \sqrt{75cm^2} = 5\sqrt{3cm^2} \approx 5\cdot 1.732cm = 8.66cm$

Answer 2

Answer:

8.7

Step-by-step explanation:

hope this help!