HMMT 二月 2006 · GEN1 赛 · 第 3 题
HMMT February 2006 — GEN1 Round — Problem 3
题目详情
- A square and an equaliteral triangle together have the property that the area of each is the perimeter of the other. Find the square’s area.
解析
- A square and an equaliteral triangle together have the property that the area of each is the perimeter of the other. Find the square’s area. √ 3 Answer: 12 4 Solution: Let s, t be the side lengths of the square and triangle, respectively. Then √ 2 3 t 4 s = , and so 4 ( ) √ 2 2 4 3 t 3 t 2 3 t = s = = , 8 16 2 √ √ 3 3 3 8 2 8 so that t = 2 and s = 3 t = 3 2 = 12 4 .