返回题库

PUMaC 2013 · 几何（B 组） · 第 6 题

PUMaC 2013 — Geometry (Division B) — Problem 6

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 6 ] Draw an equilateral triangle with center O . Rotate the equilateral triangle 30 , 60 , 90 with respect to O so there would be four congruent equilateral triangles on each other. Look at the diagram. If the smallest triangle has area 1, the area of the original equilateral triangle √ could be expressed as p + q r where p, q, r are positive integers and r is not divisible by a square greater than 1. Find p + q + r .
解析
  1. [ 6 ] Draw an equilateral triangle with center O . Rotate the equilateral triangle 30 , 60 , 90 with respect to O so there would be four congruent equilateral triangles on each other. Look at the diagram. If the smallest triangle has area 1, the area of the original equilateral triangle p could be expressed as p + q r where p, q, r are positive integers and r is not divisible by a square greater than 1. Find p + q + r . Solution Same problem exists in Test A. 102