2000 AMC 10 Problems/Problem 10
Problem
The sides of a triangle with positive area have lengths , , and . The sides of a second triangle with positive area have lengths , , and . What is the smallest positive number that is not a possible value of ?
Solution
Since and are fixed sides, the smallest possible side has to be larger than and the largest possible side has to be smaller than . This gives us the triangle inequality and . can be attained by letting and . However, cannot be attained. Thus, the answer is .
Video Solution by Daily Dose of Math
https://youtu.be/203JJbC2Clg?si=XCoDHzGHfoEDhUN7
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See Also
2000 AMC 10 (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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