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Maximum Possible Difference: Two Joined Triangles

GMAT-T1OW4F

Two triangles share a side of length $6$, forming a quadrilateral. Both triangles also have a side of length $3$.

What is the maximum possible difference between the lengths of the two unknown sides?
Round to the nearest whole number.

A

$3$

B

$4$

C

$5$

D

$6$

E

$9$