1989 AMC 12 第 17 题
先试着解答 1989 AMC 12 第 17 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1989 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
17.
一个等边三角形的周长比一个正方形的周长多 厘米。三角形的每条边都比正方形的每条边长 厘米。正方形的周长大于 。有多少个正整数不可能是 的值？
The perimeter of an equilateral triangle exceeds the perimeter of a square by cm. The length of each side of the triangle exceeds the length of each side of the square by cm. The square has perimeter greater than How many positive integers are not possible values for
无穷多个
infinitely many
小提示：
设正方形的边长为
Let the square’s side length be
大提示：
把周长为正这一条件转化为关于 的严格不等式
Translate the positive-perimeter condition into a strict inequality for
解答：
若正方形的边长为 ，则三角形的边长为 。周长条件给出 所以 。条件 等价于 。因此，正整数 至 恰好是不可能的值。
所以正确答案是 D。
If the square has side the triangle has side The perimeter condition gives so The condition is equivalent to Thus the positive integers through are precisely the impossible values.
Thus the correct answer is D.
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