HMMT 二月 2004 · GEN1 赛 · 第 5 题

英文解析

5. 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 subtractingthe second equation gives 2 xy = 10, so the area is xy = 5.