Difference between revisions of "2017 AMC 10A Problems/Problem 7"

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Let <math>j</math> represent how far Jerry walked, and <math>s</math> represent how far Sylvia walked. Since the field is a square, and Jerry walked two sides of it, while Silvia walked the diagonal, we can simply define the side of the square field to be one, and find the distances they walked. Since Jerry walked two sides,  
 
Let <math>j</math> represent how far Jerry walked, and <math>s</math> represent how far Sylvia walked. Since the field is a square, and Jerry walked two sides of it, while Silvia walked the diagonal, we can simply define the side of the square field to be one, and find the distances they walked. Since Jerry walked two sides,  
 
<math>j = 2</math>
 
<math>j = 2</math>
Since Silvia walked the diagonal, she walked the hypotenuse of a 45, 45, 90 triangle with leg length 1. Thus,
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Since Silvia walked the diagonal, she walked the hypotenuse of a <math>45</math>, <math>45</math>, <math>90</math> triangle with leg length <math>1</math>. Thus,
 
<math>s = \sqrt{2} = 1.414...</math>
 
<math>s = \sqrt{2} = 1.414...</math>
 
We can then take  
 
We can then take  
 
<math>\frac{j-s}{j} \approx \frac{2 - 1.4}{2}=0.3 \implies \boxed{\textbf{(A)}\ 30\%}</math>
 
<math>\frac{j-s}{j} \approx \frac{2 - 1.4}{2}=0.3 \implies \boxed{\textbf{(A)}\ 30\%}</math>
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==Video Solution==
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https://youtu.be/pxg7CroAt20
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https://youtu.be/MUxbCp-2OYQ
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 +
~savannahsolver
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2017|ab=A|num-b=6|num-a=8}}
 
{{AMC10 box|year=2017|ab=A|num-b=6|num-a=8}}
{{AMC12 box|year=2017|ab=A|num-b=3|num-a=5}}
 
 
{{MAA Notice}}
 
{{MAA Notice}}
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[[Category:Introductory Geometry Problems]]

Revision as of 14:04, 2 July 2020

Problem

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?

$\textbf{(A)}\ 30\%\qquad\textbf{(B)}\ 40\%\qquad\textbf{(C)}\ 50\%\qquad\textbf{(D)}\ 60\%\qquad\textbf{(E)}\ 70\%$

Solution

Let $j$ represent how far Jerry walked, and $s$ represent how far Sylvia walked. Since the field is a square, and Jerry walked two sides of it, while Silvia walked the diagonal, we can simply define the side of the square field to be one, and find the distances they walked. Since Jerry walked two sides, $j = 2$ Since Silvia walked the diagonal, she walked the hypotenuse of a $45$, $45$, $90$ triangle with leg length $1$. Thus, $s = \sqrt{2} = 1.414...$ We can then take $\frac{j-s}{j} \approx \frac{2 - 1.4}{2}=0.3 \implies \boxed{\textbf{(A)}\ 30\%}$

Video Solution

https://youtu.be/pxg7CroAt20

https://youtu.be/MUxbCp-2OYQ

~savannahsolver

See Also

2017 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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