Difference between revisions of "2008 AMC 8 Problems/Problem 6"

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==Problem==
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== Problem ==
 
In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
 
In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
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<asy>
 
<asy>
 
size((70));
 
size((70));
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fill((5,0)--(7.5,2.5)--(10,0)--(7.5,-2.5)--cycle, gray);
 
fill((5,0)--(7.5,2.5)--(10,0)--(7.5,-2.5)--cycle, gray);
 
</asy>
 
</asy>
 +
 
<math> \textbf{(A)}\ 3:10 \qquad\textbf{(B)}\ 3:8 \qquad\textbf{(C)}\ 3:7 \qquad\textbf{(D)}\ 3:5 \qquad\textbf{(E)}\ 1:1 </math>
 
<math> \textbf{(A)}\ 3:10 \qquad\textbf{(B)}\ 3:8 \qquad\textbf{(C)}\ 3:7 \qquad\textbf{(D)}\ 3:5 \qquad\textbf{(E)}\ 1:1 </math>
  
==See Also==
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== Solution ==
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Dividing the gray square into four smaller squares, there are <math>6</math> gray tiles and <math>10</math> white tiles, giving a ratio of <math>\boxed{\textbf{(D)}\ 3:5}</math>.
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== See Also ==
 
{{AMC8 box|year=2008|num-b=5|num-a=7}}
 
{{AMC8 box|year=2008|num-b=5|num-a=7}}
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{{MAA Notice}}

Revision as of 13:36, 19 October 2020

Problem

In the figure, what is the ratio of the area of the gray squares to the area of the white squares?

[asy] size((70)); draw((10,0)--(0,10)--(-10,0)--(0,-10)--(10,0)); draw((-2.5,-7.5)--(7.5,2.5)); draw((-5,-5)--(5,5)); draw((-7.5,-2.5)--(2.5,7.5)); draw((-7.5,2.5)--(2.5,-7.5)); draw((-5,5)--(5,-5)); draw((-2.5,7.5)--(7.5,-2.5)); fill((-10,0)--(-7.5,2.5)--(-5,0)--(-7.5,-2.5)--cycle, gray); fill((-5,0)--(0,5)--(5,0)--(0,-5)--cycle, gray); fill((5,0)--(7.5,2.5)--(10,0)--(7.5,-2.5)--cycle, gray); [/asy]

$\textbf{(A)}\ 3:10 \qquad\textbf{(B)}\ 3:8 \qquad\textbf{(C)}\ 3:7 \qquad\textbf{(D)}\ 3:5 \qquad\textbf{(E)}\ 1:1$

Solution

Dividing the gray square into four smaller squares, there are $6$ gray tiles and $10$ white tiles, giving a ratio of $\boxed{\textbf{(D)}\ 3:5}$.

See Also

2008 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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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