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，再向正北走到达目的地；Silvia 则朝东北方向沿直线走到目的地。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

难度评级：1200

小提示：

设边长为 $x$ ；Jerry 走 $2x$ ，Silvia 走对角线

Let the side be $x$ ; Jerry walks $2x$ and Silvia walks the diagonal

大提示：

对角线为 $x\sqrt2$ ，节省的比例是 $\dfrac{2x-x\sqrt2}{2x}=1-\dfrac{\sqrt2}{2}$ 。

The diagonal is $x\sqrt2,$ so the fraction saved is $\dfrac{2x-x\sqrt2}{2x}=1-\dfrac{\sqrt2}{2}$

解答：

如果正方形边长为 $x$ ，Jerry 走 $x+x=2x$ 而 Silvia 走对角线 $\sqrt{x^2+x^2}=x\sqrt2$ 。

Silvia 的路程短了的比例为 $\begin{aligned} &\dfrac{2x-x\sqrt2}{2x}=1-\dfrac{\sqrt2}{2} \\ &\approx 1-0.707=0.293 \end{aligned}\text{。}$

这最接近 $30\%$ 。

所以正确答案是 A。

If the square has side $x,$ Jerry walks $x+x=2x,$ while Silvia walks the diagonal $\sqrt{x^2+x^2}=x\sqrt2.$

The fraction by which Silvia’s trip is shorter is $\begin{aligned} &\dfrac{2x-x\sqrt2}{2x}=1-\dfrac{\sqrt2}{2} \\ &\approx 1-0.707=0.293. \end{aligned}$

This is closest to $30\%.$

Thus, the correct answer is A.

2017 AMC 12A 第 4 题

答案：A

难度评级：1200

小提示：

大提示：

解答：

其他年份的第 4 题