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

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==Video Solution==
 
==Video Solution==
 
Associated video: https://youtu.be/QCWOZwYVJMg
 
Associated video: https://youtu.be/QCWOZwYVJMg
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https://youtu.be/8XtEOkP-AS0
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~savannahsolver
  
 
==See Also:==
 
==See Also:==

Revision as of 12:37, 1 June 2022

Problem 11

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

https://youtu.be/8XtEOkP-AS0

~savannahsolver

See Also:

2017 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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All AJHSME/AMC 8 Problems and Solutions

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