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HMMT 二月 2015 · 冲刺赛 · 第 2 题

HMMT February 2015 — Guts Round — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  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

英文解析

  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