Question

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?

$30\%$

$40\%$

$50\%$

$60\%$

$70\%$

Solution:

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

Thus, A is the correct answer.

2017 AMC 10A Problem 7

Solution:

Problem 7 in Other Years