AMC 8 2015 Problem 8
AMC8 2015 年第 8 题
三角形★★☆☆☆
What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19 ?
一个三角形的其中两条边长度分别是 5 和 19，那么大于这个三角形周长的最小整数是多少？
- A.24
- B.29
- C.43
- D.48
- E.57
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
We know from the Triangle Inequality that the last side, , fulfills s<5+19=24. Adding 5+19 to both sides of the inequality, we get s+5+19<48, and because s+5+19 is the perimeter of our triangle, 48 is our answer.
, fulfills s<5+19=24, meaning that s<24. The greatest value of s can be 23. 23+5+19 is 47. Since 48 is our nearest answer choice, the answer is 48.-TheNerdWhoIsNerdy. minor edit by themathkidwoohooooo: the greatest value of s is 24- , where represents an infinitesimal (a constant smaller than any positive number but not zero or negative. it is between the positives and 0. another way to think of it is ). NOT 23!!!!!!!!!!!!!!!
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