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Trisected rectangle

Source:

February 3, 2016

AMCAMC 10AMC 10 Ageometryrectangle

Problem Statement

In rectangle

ABCD

,

AB=6

and

BC=3

. Point

E

between

B

and

C

, and point

F

between

E

and

C

are such that

BE=EF=FC

. Segments

\overline{AE}

and

\overline{AF}

intersect

\overline{BD}

at

P

and

Q

, respectively. The ratio

BP:PQ:QD

can be written as

r:s:t

, where the greatest common factor of

r,s

and

t

is

1

. What is

r+s+t

?

<span class='latex-bold'>(A) </span> 7 \qquad <span class='latex-bold'>(B) </span> 9 \qquad <span class='latex-bold'>(C) </span> 12 \qquad <span class='latex-bold'>(D) </span> 15 \qquad <span class='latex-bold'>(E) </span> 20

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