Question

一只旅鼠坐在边长为 $10$ 米的正方形的一个角上。它沿对角线朝对角跑了 $6.2$ 米。它停下，向右转 $90^{\circ}$ ，又跑了 $2$ 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 $10$ meters. The lemming runs $6.2$ meters along a diagonal toward the opposite corner. It stops, makes a $90^{\circ}$ right turn and runs $2$ 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?

$2$

$4.5$

$5$

$6.2$

$7$

答案：C

知识点：正方形（几何）不变量

难度评级：1550

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 $10$ 米，到两条竖直边的距离和也一样。因此 $4$ 个距离之和为 $20$ 米，平均数为 $20 \div 4 = 5$ 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 $10$ meters and the same for the vertical sides. Therefore, the $4$ distances sum to $20$ meters, making the average $20 \div 4 = 5$ meters.

Thus, C is the correct answer.

2007 AMC 8 第 22 题

答案：C

难度评级：1550

解答：

其他年份的第 22 题