MathDB
1997 AJHSME #15 - Ratio of Areas

Source:

June 30, 2011
ratiogeometryAMC

Problem Statement

Each side of the large square in the figure is trisected (divided into three equal parts). The corners of an inscribed square are at these trisection points, as shown. The ratio of the area of the inscribed square to the area of the large square is
[asy] draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((1,0)--(1,0.2)); draw((2,0)--(2,0.2)); draw((3,1)--(2.8,1)); draw((3,2)--(2.8,2)); draw((1,3)--(1,2.8)); draw((2,3)--(2,2.8)); draw((0,1)--(0.2,1)); draw((0,2)--(0.2,2)); draw((2,0)--(3,2)--(1,3)--(0,1)--cycle); [/asy]
<spanclass=latexbold>(A)</span> 33<spanclass=latexbold>(B)</span> 59<spanclass=latexbold>(C)</span> 23<spanclass=latexbold>(D)</span> 53<spanclass=latexbold>(E)</span> 79<span class='latex-bold'>(A)</span>\ \dfrac{\sqrt{3}}{3} \qquad <span class='latex-bold'>(B)</span>\ \dfrac{5}{9} \qquad <span class='latex-bold'>(C)</span>\ \dfrac{2}{3} \qquad <span class='latex-bold'>(D)</span>\ \dfrac{\sqrt{5}}{3} \qquad <span class='latex-bold'>(E)</span>\ \dfrac{7}{9}