AMC8 2007

AMC8 2007 · Q22

AMC8 2007 · Q22. It mainly tests Area & perimeter, Coordinate geometry.

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° 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?

一只旅鼠坐在边长10米的正方形的角上。它沿着对角线向对角跑了6.2米。然后停下，向右转90°，再跑2米。科学家测量旅鼠到正方形每条边的最近距离。这些四个距离的平均值是多少米？

(A) 2 2

(B) 4.5 4.5

(D) 6.2 6.2

(E) 7 7

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) Wherever the lemming is inside the square, the sum of the distances to the two horizontal sides is 10 meters and the sum of the distances to the two vertical sides is 10 meters. Therefore the sum of all four distances is 20 meters, and the average of the four distances is $\frac{20}{4}=5$ meters.

（C）无论旅鼠在正方形内的什么位置，到两条水平边的距离之和是10米，到两条竖直边的距离之和也是10米。因此四个距离的总和是20米，这四个距离的平均值为 $\frac{20}{4}=5$ 米。

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