2001 AMC 12 Problem 15
Problem 15 of 25IntermediateGeometry
An insect lives on the surface of a regular tetrahedron with edges of length It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? (Note: Two edges of a tetrahedron are opposite if they have no common endpoint.)
Answer choices
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Solution
A shortest path leaves the starting edge through one of its two incident faces and reaches the opposite edge through one of its two incident faces. Any such pair of faces shares an edge. Unfolding that pair gives a rhombus of side made of two equilateral triangles.
The two opposite-edge midpoints become the midpoints of opposite sides of this rhombus, which are exactly unit apart along a straight segment. Folding back preserves the length, so the shortest trip is
Thus, the correct answer is B.