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Difference between revisions of "2017 AMC 8 Problems/Problem 11"

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==Problem 11==
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==Problem==
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A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor? what does diagonals mean
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A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?
  
  
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Since the number of tiles lying on both diagonals is <math>37</math>, counting one tile twice, there are <math>37=2x-1\implies x=19</math> tiles on each side. Hence, our answer is <math>19^2=361=\boxed{\textbf{(C)}\ 361}</math>.
 
Since the number of tiles lying on both diagonals is <math>37</math>, counting one tile twice, there are <math>37=2x-1\implies x=19</math> tiles on each side. Hence, our answer is <math>19^2=361=\boxed{\textbf{(C)}\ 361}</math>.
  
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==See Also==
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==Video Solution==
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Associated video: https://youtu.be/QCWOZwYVJMg
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==See Also:==
 
{{AMC8 box|year=2017|num-b=10|num-a=12}}
 
{{AMC8 box|year=2017|num-b=10|num-a=12}}
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 14:01, 18 January 2021

Problem

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?


$\textbf{(A) }148\qquad\textbf{(B) }324\qquad\textbf{(C) }361\qquad\textbf{(D) }1296\qquad\textbf{(E) }1369$

Solution

Since the number of tiles lying on both diagonals is $37$, counting one tile twice, there are $37=2x-1\implies x=19$ tiles on each side. Hence, our answer is $19^2=361=\boxed{\textbf{(C)}\ 361}$.

Video Solution

Associated video: https://youtu.be/QCWOZwYVJMg

See Also:

2017 AMC 8 (Problems • Answer Key • Resources)
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Problem 10 		Followed by
Problem 12
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