1987 AHSME Problems/Problem 25
Revision as of 11:56, 31 March 2018 by Hapaxoromenon (talk | contribs) (Added a solution with explanation)
Problem
is a triangle:
and both the coordinates of
are integers. What is the minimum area
can have?
Solution
Let have coordinates
. Then by the Shoelace Formula, the area of
is
. Since
and
are integers,
is a positive integer, and by Bezout's Lemma, it can equal
(e.g. with
), so the minimum area is
, which is answer
.
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.