AMC8 2015
AMC8 2015 · Q8
AMC8 2015 · Q8. It mainly tests Triangles (properties).
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?
有一个边长为 5 和边长为 19 的三角形，其周长的上确界（大于该周长的最小整数）是多少？
(A)
24
24
(B)
29
29
(C)
43
43
(D)
48
48
(E)
57
57
Answer
Correct choice: (D)
正确答案：（D）
Solution
Answer (D): Let $t$ be the length of the third side of the triangle. By the Triangle Inequality, $t<5+19=24$. So the perimeter $5+19+t<5+19+(5+19)=48$.
答案（D）：设 $t$ 为三角形第三边的长度。由三角形不等式可得 $t<5+19=24$。因此周长满足 $5+19+t<5+19+(5+19)=48$。
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