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

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 $\begin{aligned} \dfrac{2s - s\sqrt{2}}{2s} &= \dfrac{2 - \sqrt{2}}{2} \\ &\approx \dfrac{2 - 1.4}{2} \\&= .3\\ &= 30\%. \end{aligned}$

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 $\begin{aligned} \dfrac{2s - s\sqrt{2}}{2s} &= \dfrac{2 - \sqrt{2}}{2} \\ &\approx \dfrac{2 - 1.4}{2} \\&= .3\\ &= 30\%. \end{aligned}$

Thus, A is the correct answer.

2017 AMC 10A 第 7 题

答案：A

难度评级：960

解答：

其他年份的第 7 题