2017 AMC 8 第 16 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。
16.
在下图中，在边 上选择点 ，使得 和 的周长相等。 的面积是多少？
In the figure shown below, choose point on side so that and have equal perimeters. What is the area of
小提示：
用周长相等条件求 和
Use the equal-perimeter condition to find and .
大提示：
一旦 被分割，两个三角形从 引出的高相同，所以面积按底边长度比较
Once is split, the two triangles have the same altitude from , so compare areas by base lengths.
视频讲解：
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文字解答：
要使两个三角形周长相等， 必须分成 和 。
和 有相同的高，所以面积与底边长度成比例。这说明 的面积是 倍的 的面积，即
所以正确答案是 D。
The only way to split into two parts such that the two triangles have the same perimeter is if and
and have the same altitudes, so their areas are proportional to their bases. This means that the area of is the area of which is
Thus, D is the correct answer.
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