Answer:
The length of each side of the polyhedron, s is 4.142 or
= [tex]10(\sqrt{2}-1)[/tex]
Step-by-step explanation:
If we take the distance of the length of the side of the cube where Donatello make the cut to the corner of the cube as x we get the side of length each polyhedron as
[tex]\sqrt{x^2 + x^2} = \sqrt{2x^2} =x\sqrt{2}[/tex]
x·√2 because we have an hy
Therefore, the original cube had sides of length
10 = 2·x + x·√2
Solving for x we get
[tex]x = \frac{10}{\sqrt{2}+2 }[/tex]
Therefore the length of s is x·√2 which gives
[tex]s = x\sqrt{2} = \frac{10}{\sqrt{2}+2 }\sqrt{2} = 10\sqrt{2} -10 = 10(\sqrt{2}-1) = 4.142[/tex]
The length of each side of the polyhedron, s = 4.142.
