2012 AMC 8 第 25 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。
25.
一个面积为 的正方形内接于一个面积为 的正方形，较小正方形的每个顶点分别在较大正方形的一条边上。较小正方形的一个顶点将较大正方形的一条边分成两段，长度分别为 和 。 的值是多少？
A square with area is inscribed in a square with area , with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length and the other of length . What is the value of
小提示：
两个正方形之间的面积被分成四个全等直角三角形。
The area between the squares is split into four congruent right triangles.
大提示：
每个小三角形的面积是 。
Each small triangle has area .
视频讲解：
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文字解答：
四个三角形都可以通过旋转互相得到，所以它们全等。因此可以如图标出 。两个正方形之间的总面积为 ，所以有 个全等三角形的总面积为 。每个三角形面积为 。每个三角形的面积也等于 ，所以 。因此 。
所以正确答案是 C。
Since all the triangles can be made from each other by rotating them around, they are all congruent. Therefore, we can place the as we have. The total area of the triangles is so we have congruent triangles with a combined area of This means the area of each triangle is The area of each triangle is also so This means
Thus, the correct answer is C .
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