HMMT 二月 2000 · 几何 · 第 2 题
HMMT February 2000 — Geometry — Problem 2
题目详情
- In a triangle the sum of squares of the sides is 96. What is the maxim um p ossible v alue of the sum of the medians?
解析
- The maxim um o urs in an equilateral triangle, in whi h ase the sides a = b are p p p 2 2 2 2 a 3 giv en b y a + b + = 3 a = 96, so a = 4 2. Th us, the medians are 3 ( ) = 6 6 . 2 2