MathDB

Purple Comet 2009 HS Problem 14

Source:

August 3, 2011

geometrytrapezoidrationumber theoryrelatively prime

Problem Statement

Let

ABCD

be a trapezoid with

AB

parallel to

CD, AB

has length

1,

and

CD

has length

41.

Let points

X

and

Y

lie on sides

AD

and

BC,

respectively, such that

XY

is parallel to

CDXY

and

CD,

and

XY

has length

31.

Let

m

and

n

be two relatively prime positive integers such that the ratio of the area of

ABYX

to the area of

CDXY

is

\tfrac{m}{n}.

Find

m+2n.

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