MathDB

24

Part of 2013 AMC 8

Problems(1)

2013/8/24/Three squares

Source:

11/27/2013
Squares ABCDABCD, EFGHEFGH, and GHIJGHIJ are equal in area. Points CC and DD are the midpoints of sides IHIH ad HEHE, respectively. What is the ratio of the area of the shaded pentagon AJICBAJICB to the sum of the areas of the three squares?
[asy] pair A,B,C,D,E,F,G,H,I,J; A = (0.5,2); B = (1.5,2); C = (1.5,1); D = (0.5,1); E = (0,1); F = (0,0); G = (1,0); H = (1,1); I = (2,1); J = (2,0); draw(A--B); draw(C--B); draw(D--A); draw(F--E); draw(I--J); draw(J--F); draw(G--H); draw(A--J); filldraw(A--B--C--I--J--cycle,grey); draw(E--I); dot("AA", A, NW); dot("BB", B, NE); dot("CC", C, NE); dot("DD", D, NW); dot("EE", E, NW); dot("FF", F, SW); dot("GG", G, S); dot("HH", H, N); dot("II", I, NE); dot("JJ", J, SE);[/asy]
<spanclass=latexbold>(A)</span> 14<spanclass=latexbold>(B)</span> 724<spanclass=latexbold>(C)</span> 13<spanclass=latexbold>(D)</span> 38<spanclass=latexbold>(E)</span> 512<span class='latex-bold'>(A)</span>\ \frac14 \qquad <span class='latex-bold'>(B)</span>\ \frac7{24} \qquad <span class='latex-bold'>(C)</span>\ \frac13 \qquad <span class='latex-bold'>(D)</span>\ \frac38 \qquad <span class='latex-bold'>(E)</span>\ \frac5{12}
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