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PUMaC 2016 · 团队赛 · 第 1 题

PUMaC 2016 — Team Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. (3) Quadrilateral ABCD has integer side lengths, and angles ABC , ACD , and BAD are right angles. Compute the smallest possible value of AD .
解析
  1. Let AB = a , BC = b , and AC = c . Then by similar triangles, CD = c · and AD = . b b ( a, b, c ) must be a Pythagorean triple, from which it can easily be found that the smallest 2 c possible value of is 25 . b Problem written by Eric Neyman. ◦ ◦