PUMaC 2012 · 团队赛 · 第 2 题
PUMaC 2012 — Team Round — Problem 2
题目详情
- (2 digits) ABCDE is a pentagon with AB = BC = CD = 2, ∠ ABC = ∠ BCD = 120 degrees, and ∠ BAE = ∠ CDE = 105 degrees. Find the area of triangle 4 BDE . Your answer √ a + b in its simplest form can be written as , where where a, b, c are integers and b is square-free. c Find abc .
解析
- Problem: (2 digits) ABCDE is a pentagon with AB = BC = CD = 2, ∠ ABC = ∠ BCD = 120 degrees, and ∠ BAE = ∠ CDE = 105 degrees. Find the area of triangle 4 BDE . Your √ a + b answer in its simplest form can be written as , where where a, b, c are integers and b is c square-free. Find abc . Answer: 18 4 Solution: Subtract the areas of triangles EAB and CDE from the area of the pentagon. The √ answer should be (3 + 3) / 2, so abc = 18 . Author: Ante