2000 AMC 10 竞赛试题/第10题
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 
.
AEIS在线试听课程
