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HMMT 二月 2000 · 几何 · 第 2 题

HMMT February 2000 — Geometry — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. In a triangle the sum of squares of the sides is 96. What is the maxim um p ossible v alueof the sum of the medians?

英文原题

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? 3. Find P B , giv en that P A = 15 ; P C = 20 ; P D = 7, and AB C D is a square.
D C
B A aaaaa C C C C ##### P 4. Find the total area of the non-triangle regions in the gure b elo w (the shaded area). b/3
a/4
a/3
a
b

解析

英文解析

  1. The maxim um o urs in an equilateral triangle, in which ase the sides a = b arep
    2 2 2 2 a 3 ppgiv en b y a + b + = 3 a = 96, so a = 4 2. Th us, the medians are 3 ( ) = 6 6 .
    22