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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 29, 2017
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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?

$$Sum \ of \ the \ lengths\\=\sqrt{3^2+2^2}+\sqrt{3^2+4^2}+\sqrt{2^2+4^2}\\=\sqrt{13}+\sqrt{25}+\sqrt{20}\\=\sqrt{12}+5+2\cdot \sqrt{5}$$

$$Sum \ of \ the \ lengths=12.936$$

!

asinus  Apr 29, 2017