MathDB

Points

B

D

, and

J

are midpoints of the sides of right triangle

ACG

. Points

K

E

I

are midpoints of the sides of triangle , etc. If the dividing and shading process is done 100 times (the first three are shown) and

AC=CG=6

, then the total area of the shaded triangles is nearest [asy] draw((0,0)--(6,0)--(6,6)--cycle); draw((3,0)--(3,3)--(6,3)); draw((4.5,3)--(4.5,4.5)--(6,4.5)); draw((5.25,4.5)--(5.25,5.25)--(6,5.25)); fill((3,0)--(6,0)--(6,3)--cycle,black); fill((4.5,3)--(6,3)--(6,4.5)--cycle,black); fill((5.25,4.5)--(6,4.5)--(6,5.25)--cycle,black); label("

A

",(0,0),SW); label("

B

",(3,0),S); label("

C

",(6,0),SE); label("

D

",(6,3),E); label("

E

",(6,4.5),E); label("

F

",(6,5.25),E); label("

G

",(6,6),NE); label("

H

",(5.25,5.25),NW); label("

I

",(4.5,4.5),NW); label("

J

",(3,3),NW); label("

K

",(4.5,3),S); label("

L

",(5.25,4.5),S);[/asy]

\text{(A)}\ 6\qquad\text{(B)}\ 7\qquad\text{(C)}\ 8\qquad\text{(D)}\ 9\qquad\text{(E)}\ 10

25

Problems(1)