AMC 8 2005 Problem 15
AMC8 2005 年第 15 题
三角形★★★☆☆
How many different isosceles triangles have integer side lengths and perimeter 23?
有多少个不同的等腰三角形，满足各边长度均为整数，且周长为 23?
- A.2
- B.4
- C.6
- D.9
- E.11
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Because the perimeter of such a triangle is 23 23, and the sum of the two equal side lengths is even, the length of the base is odd. Also, the length of the base is less than the sum of the other two side lengths, so it is less than half of 23 23. Thus the six possible triangles have side lengths 1, 11, 11; 3, 10, 10; 5, 9, 9 1,11,11;3,10,10;5,9,9; 7, 8, 8; 9, 7, 7 7,8,8;9,7,7 and 11, 6, 6 11,6,6. Answer: 𝐶 C .
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