Difference between revisions of "2020 AMC 8 Problems/Problem 24"
Icematrix2 (talk | contribs) (Created page with "A large square region is paved with <math>n^2</math> gray square tiles, each measuring <math>s</math> inches on a side. A border <math>d</math> inches wide surrounds each tile...") |
Icematrix2 (talk | contribs) |
||
| Line 13: | Line 13: | ||
filldraw((9,9)--(12,9)--(12,12)--(9,12)--cycle, mediumgray); | filldraw((9,9)--(12,9)--(12,12)--(9,12)--cycle, mediumgray); | ||
</asy> | </asy> | ||
| − | |||
| − | |||
<math>\textbf{(A) }\frac{6}{25} \qquad \textbf{(B) }\frac{1}{4} \qquad \textbf{(C) }\frac{9}{25} \qquad \textbf{(D) }\frac{7}{16} \qquad \textbf{(E) }\frac{9}{16}</math> | <math>\textbf{(A) }\frac{6}{25} \qquad \textbf{(B) }\frac{1}{4} \qquad \textbf{(C) }\frac{9}{25} \qquad \textbf{(D) }\frac{7}{16} \qquad \textbf{(E) }\frac{9}{16}</math> | ||
Revision as of 22:17, 17 November 2020
A large square region is paved with 
gray square tiles, each measuring 
inches on a side. A border 
inches wide surrounds each tile. The figure below shows the case for 
. When 
, the 
gray tiles cover 
of the area of the large square region. What is the ratio 
for this larger value of 
![[asy] draw((0,0)--(13,0)--(13,13)--(0,13)--cycle); filldraw((1,1)--(4,1)--(4,4)--(1,4)--cycle, mediumgray); filldraw((1,5)--(4,5)--(4,8)--(1,8)--cycle, mediumgray); filldraw((1,9)--(4,9)--(4,12)--(1,12)--cycle, mediumgray); filldraw((5,1)--(8,1)--(8,4)--(5,4)--cycle, mediumgray); filldraw((5,5)--(8,5)--(8,8)--(5,8)--cycle, mediumgray); filldraw((5,9)--(8,9)--(8,12)--(5,12)--cycle, mediumgray); filldraw((9,1)--(12,1)--(12,4)--(9,4)--cycle, mediumgray); filldraw((9,5)--(12,5)--(12,8)--(9,8)--cycle, mediumgray); filldraw((9,9)--(12,9)--(12,12)--(9,12)--cycle, mediumgray); [/asy]](http://latex.artofproblemsolving.com/c/0/d/c0d420afb8c2f467480a85d6c02e403e50af81a8.png)
