MathDB
Rectangle cut into two hexagons

Source: AMC 12 2006A, Problem 6

February 5, 2006
geometryrectanglerotationAMC

Problem Statement

The 8×18 8\times 18 rectangle ABCD ABCD is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is y y? [asy] unitsize(2mm); defaultpen(fontsize(10pt)+linewidth(.8pt)); dotfactor=4; draw((0,4)--(18,4)--(18,-4)--(0,-4)--cycle); draw((6,4)--(6,0)--(12,0)--(12,-4)); label("DD",(0,4),NW); label("CC",(18,4),NE); label("BB",(18,-4),SE); label("AA",(0,-4),SW); label("yy",(9,1)); [/asy]<spanclass=latexbold>(A)</span>6<spanclass=latexbold>(B)</span>7<spanclass=latexbold>(C)</span>8<spanclass=latexbold>(D)</span>9<spanclass=latexbold>(E)</span>10 <span class='latex-bold'>(A) </span> 6\qquad <span class='latex-bold'>(B) </span> 7\qquad <span class='latex-bold'>(C) </span> 8\qquad <span class='latex-bold'>(D) </span> 9\qquad <span class='latex-bold'>(E) </span> 10