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
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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
.
See also
2003 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |