Question 1152809
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Let x be the distance from a corner of the cube to where the cut is made to slice off each pyramid.  Then the length of each side of the new polyhedron is {{{x*sqrt(2)}}}.<br>
Each side of the original cube is then made up of two segments of length x and one of length {{{x*sqrt(2)}}}.<br>
{{{10 = 2x+x*sqrt(2)}}}
{{{10 = x(2+sqrt(2))}}}
{{{x = 10/(2+sqrt(2)) = 10(2-sqrt(2))/2 = 5(2-sqrt(2)) = 10-5sqrt(2)}}}<br>
The side length s of the new polyhedron is<br>
{{{x*sqrt(2) = (10-5sqrt(2))*sqrt(2) = 10sqrt(2)-10 = 10(sqrt(2)-1)}}}<br>