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HMMT 二月 2015 · 冲刺赛 · 第 2 题

HMMT February 2015 — Guts Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] Let ABCDE be a convex pentagon such that ∠ ABC = ∠ ACD = ∠ ADE = 90 and AB = BC = CD = DE = 1. Compute AE . 2
解析
  1. [ 4 ] Let ABCDE be a convex pentagon such that ∠ ABC = ∠ ACD = ∠ ADE = 90 and AB = BC = CD = DE = 1. Compute AE . Answer: 2 By Pythagoras, 2 2 2 2 AE = AD + 1 = AC + 2 = AB + 3 = 4 , so AE = 2. 2