2017 AMC 10A Problems/Problem 10
Contents
[hide]Problem
Joy has thin rods, one each of every integer length from cm through cm. She places the rods with lengths cm, cm, and cm 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 triangle inequality generalizes to all polygons, so and to get . Now, we know that there are numbers between and exclusive, but we must subtract to account for the 2 lengths already used that are between those numbers, which gives
Video Solution
See Also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |
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