2007 AMC 8 第 22 题
先试着解答 2007 AMC 8 第 22 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 2007 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。
22.
一只旅鼠坐在边长为 米的正方形的一个角上。它沿对角线朝对面的顶点跑了 米。它停下，向右转 ，又跑了 米。一位科学家测量旅鼠到正方形每条边的最短距离。这四个距离的平均数是多少米？
A lemming sits at a corner of a square with side length meters. The lemming runs meters along a diagonal toward the opposite corner. It stops, makes a right turn and runs more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?
小提示：
对正方形内任一点，到两条相对边的距离和等于边长
For any point inside a square, distances to opposite sides add to the side length.
大提示：
对两组相对边分别应用这个想法
Apply that idea to both pairs of opposite sides.
解答：
根据题目给出的长度，旅鼠停下后仍在正方形内。
因为旅鼠仍在正方形内，它到两条水平边的距离和为 米，到两条竖直边的距离和也一样。因此 个距离之和为 米，平均数为 米。
所以正确答案是 C。
Based on the lengths given in the problem, the lemming is still in the square after it stops.
Since the lemming is still in the square, the sum of the distances to the horizontal sides is meters and the same for the vertical sides. Therefore, the distances sum to meters, making the average meters.
Thus, C is the correct answer.
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