Betsy's Flag
Source:
February 11, 2008
geometry
Problem Statement
Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let be the total area of the blue triangles, the total area of the white squares, and the area of the red square. Which of the following is correct?
[asy]unitsize(3mm);
fill((-4,-4)--(-4,4)--(4,4)--(4,-4)--cycle,blue);
fill((-2,-2)--(-2,2)--(2,2)--(2,-2)--cycle,red);
path onewhite=(-3,3)--(-2,4)--(-1,3)--(-2,2)--(-3,3)--(-1,3)--(0,4)--(1,3)--(0,2)--(-1,3)--(1,3)--(2,4)--(3,3)--(2,2)--(1,3)--cycle;
path divider=(-2,2)--(-3,3)--cycle;
fill(onewhite,white);
fill(rotate(90)*onewhite,white);
fill(rotate(180)*onewhite,white);
fill(rotate(270)*onewhite,white);[/asy]
(A)\ B \equal{} W \qquad (B)\ W \equal{} R \qquad (C)\ B \equal{} R \qquad (D)\ 3B \equal{} 2R \qquad (E)\ 2R \equal{} W