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HMMT 二月 2004 · GEN1 赛 · 第 5 题

HMMT February 2004 — GEN1 Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. A rectangle has perimeter 10 and diagonal 15. What is its area?
解析
  1. A rectangle has perimeter 10 and diagonal 15. What is its area? Solution: 5 √ √ 2 2 If the sides are x and y , we have 2 x + 2 y = 10, so x + y = 5, and x + y = 15, so 2 2 2 2 x + y = 15. Squaring the first equation gives x + 2 xy + y = 25, and subtracting the second equation gives 2 xy = 10, so the area is xy = 5.