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2017 AMC 10A Problem 7

Problem 7 of 25EasierGeometryArithmetic

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?

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Solution

Let ss be the side length of the field. Then Jerry traveled 2s2s and Silvia traveled s2s\sqrt{2} from the Pythagorean theorem. The desired value is 2s−s22s=2−22≈2−1.42=0.3=30%.\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.
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Tagged: Pythagorean Theorem · percentage · estimation

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