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HMMT 十一月 2008 · 冲刺赛 · 第 11 题

HMMT November 2008 — Guts Round — Problem 11

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 8 ] Al has a rectangle of integer side lengths a and b , and area 1000. What is the smallest perimeter it could have?
解析
  1. [ 8 ] Al has a rectangle of integer side lengths a and b , and area 1000. What is the smallest perimeter it could have? Answer: 130 To minimize the sum of the side lengths, we need to keep the height and width as close as possible, because the square has the smallest perimeter of all rectangles with a fixed area. So, 40 and 25 multiply to 1000 and are as close as possible - the 40x25 rectangle has perimeter 130.