1997 AMC 8 第 15 题
先试着解答 1997 AMC 8 第 15 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 1997 AMC 8 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。
15.
图中大正方形的每条边都被三等分。内接正方形的顶点在这些三等分点上，如图所示。内接正方形面积与大正方形面积的比是
Each side of the large square in the figure is trisected (divided into three equal parts). The corners of an inscribed square are at these trisection points, as shown. The ratio of the area of the inscribed square to the area of the large square is
小提示：
用勾股定理求内接正方形的边长
Use the Pythagorean theorem for the inscribed square side
大提示：
设大正方形边长被分成三段相等的长度
Let the large square side be split into three equal parts
解答：
设大正方形边长为 。于是内接正方形的边长可以由 根据勾股定理求出。
大正方形面积为 内接正方形面积为
因此面积比为 。
所以正确答案是 B。
Let be the side length of the large square. Then we can find the side length of the inner square via from the Pythagorean Theorem.
The area of the larger square is and that of the inner square is
The ratio of the areas is then
Thus, B is the correct answer.
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