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 28, 2017

#1**+1 **

Use Pythagoras theorem to find the lengths of blue lines.

Total length

= 4/2 + 6/2 + 8/2 + \(\sqrt{(\dfrac{4}{2})^2+(\dfrac{6}{2})^2}+\sqrt{(\dfrac{8}{2})^2+(\dfrac{4}{2})^2}+\sqrt{(\dfrac{6}{2})^2+(\dfrac{8}{2})^2}\)

= 2 + 3 + 4 + \(\sqrt{13}\) + \(2\sqrt{5}\) + 5

= 14 + sqrt(13) + 2sqrt(5)

MaxWong
Apr 28, 2017