2017 AMC 12A Problems/Problem 6
Problem
Joy has thin rods, one each of every integer length from
through
. She places the rods with lengths
,
, and
on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
Solution
The quadrilateral cannot be a straight line. Thus, the fourth side must be longer than and shorter than
= 25. This means Joy can use the 19 possible integer rod lengths that fall into
. However, she has already used the rods of length
cm and
cm so the answer is
See Also
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.