MathDB
Congruent squares and pentagons

Source:

December 3, 2005
percentgeometry

Problem Statement

The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to <spanclass=latexbold>(A)</span> 50<spanclass=latexbold>(B)</span> 52<spanclass=latexbold>(C)</span> 54<spanclass=latexbold>(D)</span> 56<spanclass=latexbold>(E)</span> 58 <span class='latex-bold'>(A)</span> \ 50 \qquad <span class='latex-bold'>(B)</span> \ 52 \qquad <span class='latex-bold'>(C)</span> \ 54 \qquad <span class='latex-bold'>(D)</span> \ 56 \qquad <span class='latex-bold'>(E)</span> \ 58 \qquad [asy]unitsize(3mm); defaultpen(linewidth(0.8pt));
path p1=(0,0)--(3,0)--(3,3)--(0,3)--(0,0); path p2=(0,1)--(1,1)--(1,0); path p3=(2,0)--(2,1)--(3,1); path p4=(3,2)--(2,2)--(2,3); path p5=(1,3)--(1,2)--(0,2); path p6=(1,1)--(2,2); path p7=(2,1)--(1,2); path[] p=p1^^p2^^p3^^p4^^p5^^p6^^p7; for(int i=0; i<3; ++i) { for(int j=0; j<3; ++j) { draw(shift(3*i,3*j)*p); } }[/asy]