2015 AMC 12A 第 2 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
2.
一个三角形的三条边中有两条分别为 和 。下列哪个数不可能是这个三角形的周长？
Two of the three sides of a triangle are and Which of the following numbers is not a possible perimeter of the triangle?
小提示：
第三边严格介于 和 之间
The third side lies strictly between and
大提示：
把 加到这个范围上，就能得到周长的范围
Add to that range to bound the perimeter
解答：
根据三角形不等式，第三边 满足 ，也就是 。
周长为 ，所以它严格介于 和 之间。选项中只有 落在这个范围之外。
因此，正确答案是 E。
By the Triangle Inequality, the third side satisfies that is
The perimeter is so it lies strictly between and Among the choices, only falls outside this range.
Thus, the correct answer is E.
其他年份的第 2 题
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