2017 AMC 10A 第 7 题

Question

Jerry 和 Silvia 想从一块正方形田地的西南角走到东北角。Jerry 先向正东走，再向正北走到达目标；Silvia 则向东北方向沿直线到达目标。与 Jerry 的路程相比，Silvia 的路程大约短了多少？

Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia’s trip was, compared to Jerry’s trip?

30\%

40\%

50\%

60\%

70\%

答案：A

知识点：勾股定理百分数估算

难度评级：960

小提示：

设正方形边长为

s

。

Let the square side length be

s

大提示：

把

2s

与

s\sqrt2

的差作为 Jerry 路程的百分比。

Compare

2s

with

s\sqrt2

as a percent of Jerry’s trip

解答：

设正方形边长为

s

。Jerry 的路程是

2s

，Silvia 的直线路程是

s\sqrt{2}

。

因此 Silvia 比 Jerry 少走的比例为

\begin{aligned} \dfrac{2s - s\sqrt{2}}{2s} &= \dfrac{2 - \sqrt{2}}{2} \\ &\approx \dfrac{2 - 1.4}{2} \\&= 0.3\\ &= 30\% \end{aligned}\text{。}

所以正确答案是 A。

Let

s

be the side length of the field. Then Jerry traveled

2s

and Silvia traveled

s\sqrt{2}

from the Pythagorean theorem.

The desired value is

\begin{aligned} \dfrac{2s - s\sqrt{2}}{2s} &= \dfrac{2 - \sqrt{2}}{2} \\ &\approx \dfrac{2 - 1.4}{2} \\&= 0.3\\ &= 30\%. \end{aligned}

Thus, A is the correct answer.

2017 AMC 10A 第 7 题

答案：A

难度评级：960

小提示：

大提示：

解答：

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