2003 AIME I Problems/Problem 12
Problem
In convex quadrilateral and
The perimeter of
is 640. Find
(The notation
means the greatest integer that is less than or equal to
)
Solution
Let so
. Let
so by the Law of Cosines in
at angle
and in
at angle
,
. Then
and grouping the
terms gives
.
Since ,
and thus
so
and so
.