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PUMaC 2009 · 几何（B 组） · 第 4 题

PUMaC 2009 — Geometry (Division B) — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. Tetrahedron ABCD has sides of lengths, in increasing order, 7, 13, 18, 27, 36, 41. If AB = 41, then what is the length of CD ? ◦
解析
  1. 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. ◦