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A 4" by 6" by 8" rectangular solid is cut by slicing through the midpoint of three adjacent edges. What is the number of inches in the sum of the lengths of the edges of the tetrahedron that is cut?

waffles  Apr 30, 2017
 #1
avatar+7266 
+3

Maybe this will help:

 

sum of tetrahedron edges = red line + orange line + yellow line + green line + blue line + purple line

 

red line = \(\sqrt{3^2+2^2}=\sqrt{13}\)

orange line = \(\sqrt{3^2+4^2}=\sqrt{25}=5\)

yellow line = \(\sqrt{2^2+4^2}=\sqrt{20}=2\sqrt5\)

 

sum of tetrahedron edges = \(\sqrt{13}+5+2\sqrt5+3+2+4=14+\sqrt{13}+2\sqrt{5} \approx 22.078\)

hectictar  Apr 30, 2017
 #2
avatar+93346 
+2

Excellent answer Hectictar :)

Melody  Apr 30, 2017
 #3
avatar+7266 
+2

Thank you! It helped that I read MaxWong's answer to it the other day :)

hectictar  Apr 30, 2017

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