MathDB

In the diagram below,

ABCD

is a rectangle with side lengths

AB=3

and

BC=11

, and

AECF

is a rectangle with side lengths

AF=7

and

FC=9,

as shown. The area of the shaded region common to the interiors of both rectangles is

\frac mn

, where

m

and

n

are relatively prime positive integers. Find

m+n

.
[asy] pair A, B, C, D, E, F; A = (0,3); B=(0,0); C=(11,0); D=(11,3); E=foot(C, A, (9/4,0)); F=foot(A, C, (35/4,3)); draw(A--B--C--D--cycle); draw(A--E--C--F--cycle); filldraw(A--(9/4,0)--C--(35/4,3)--cycle,gray*0.5+0.5*lightgray); dot(A^^B^^C^^D^^E^^F); label("

A

", A, W); label("

B

", B, W); label("

C

", C, (1,0)); label("

D

", D, (1,0)); label("

F

", F, N); label("

E

", E, S); [/asy]

Problem Statement