Final answer:
The sum of the lengths of the edges of the tetrahedron that is cut is 18".
Step-by-step explanation:
The tetrahedron will have four triangular faces, each formed by cutting through the midpoint of one of the edges of the original rectangular solid. The length of each edge of the tetrahedron can be determined by observing the right triangles formed by the cuts.
Consider the right triangle formed by the midpoint of one edge, the vertex of the tetrahedron, and the midpoint of the opposite edge. This right triangle is similar to the original rectangular solid, with a scale factor of 0.5.
Therefore, the edges of the tetrahedron are half the length of the corresponding edges of the original rectangular solid.
Given that the original rectangular solid has dimensions of 4" by 6" by 8", the edges of the tetrahedron will be 2" by 3" by 4".
Now, to find the sum of the lengths of the edges of the tetrahedron, we simply add up the lengths of all four edges:
2" + 3" + 4" + 3" + 4" + 2" = 18 inches
Therefore, the sum of the lengths of the edges of the tetrahedron is 18 inches.