PUMaC 2009 · 几何（A 组） · 第 2 题
PUMaC 2009 — Geometry (Division A) — Problem 2
题目详情
- Tetrahedron ABCD havs sides of lengths, in increasing order, 7, 13, 18, 27, 36, 41. If AB = 41, then what is the length of CD ? ◦
解析
- Tetrahedron ABCD havs sides of lengths, in increasing order, 7, 13, 18, 27, 36, 41. If AB = 41, then what is the length of CD ? Solution. 13. By triangle inequality, AB + DB > 41, and AC + CB > 41. Hence, one of the pairs AD, DB and { AC, CB } must be { 18, 27 } , the other pair contains 36. WLOG, let AC = 27, CB = 18. Then DB 6 = 36, otherwise, CD > 18. Hence AD = 36, CD = 13. ◦