Difference between revisions of "2011 AMC 8 Problems/Problem 19"

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==Solution==
 
==Solution==
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The figure can be divided into <math>7</math> sections. The number of rectangles with just one section is <math>3.</math> The number of rectangles with two sections is <math>5.</math> There are none with only three sections. The number of rectangles with four sections is <math>3.</math>
  
The figure can be divided into <math>7</math> sections. The number of rectangles with just one section is <math>3.</math> The number of rectangles with two sections is <math>5.</math> There are none with only three sections. The number of rectangles with four sections is <math>3.</math> <math>3+5+3=\boxed{\textbf{(D)}\ 11}</math>
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<math>3+5+3=\boxed{\textbf{(D)}\ 11}</math>
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==Count by Reduction==
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We can remove the 3 big blocks of rectangles one by one. 7 (left) + 3 (bottom) + 1 = 11 are removed in total.
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~aliciawu
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==Video Solution 1 by SpreadTheMathLove==
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https://www.youtube.com/watch?v=mYn6tNxrWBU
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==Video Solution by WhyMath==
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https://youtu.be/IEeJsGh3ltk
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2011|num-b=18|num-a=20}}
 
{{AMC8 box|year=2011|num-b=18|num-a=20}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 10:06, 18 November 2024

Problem

How many rectangles are in this figure?

[asy] pair A,B,C,D,E,F,G,H,I,J,K,L; A=(0,0); B=(20,0); C=(20,20); D=(0,20); draw(A--B--C--D--cycle); E=(-10,-5); F=(13,-5); G=(13,5); H=(-10,5); draw(E--F--G--H--cycle); I=(10,-20); J=(18,-20); K=(18,13); L=(10,13); draw(I--J--K--L--cycle);[/asy]

$\textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12$

Solution

The figure can be divided into $7$ sections. The number of rectangles with just one section is $3.$ The number of rectangles with two sections is $5.$ There are none with only three sections. The number of rectangles with four sections is $3.$

$3+5+3=\boxed{\textbf{(D)}\ 11}$

Count by Reduction

We can remove the 3 big blocks of rectangles one by one. 7 (left) + 3 (bottom) + 1 = 11 are removed in total.

~aliciawu

Video Solution 1 by SpreadTheMathLove

https://www.youtube.com/watch?v=mYn6tNxrWBU

Video Solution by WhyMath

https://youtu.be/IEeJsGh3ltk

See Also

2011 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
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 AJHSME/AMC 8 Problems and Solutions

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