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
Answer Choices:
A.
B.
C.
D.
E.
Solution:
By the Triangle Inequality, each of and can be any number strictly between and , so . Therefore, the smallest positive number that is not a possible value of is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions