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HMMT 十一月 2013 · 冲刺赛 · 第 6 题

HMMT November 2013 — Guts Round — Problem 6

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] A right triangle has area 5 and a hypotenuse of length 5. Find its perimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT NOVEMBER 2013, 9 NOVEMBER 2013 — GUTS ROUND
解析
  1. [ 6 ] A right triangle has area 5 and a hypotenuse of length 5. Find its perimeter. √ √ 2 2 2 2 Answer: 5 + 3 5 If x, y denote the legs, then xy = 10 and x + y = 25, so x + y + x + y = √ √ √ 2 2 ( x + y ) + 2 xy + 5 = 45 + 5 = 5 + 3 5.