SAT数学Problem Solving练习题（43）
- 2017年07月27日14:04 来源：互联网
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Question 43: If a, b and c are the sides of any triangle, which of the following inequalities is not true?
(a) a·b > 0
(b) a + b > c
(c) a + c/2 >b
(d) b + c > a
(e) (a + b)·(b + c) > a·c
Answer: The first answer is true, since the product of 2 positive reals will be positive.
The second and the fourth answers are also true, since the sum of 2 sides of a triangle is always higher than the third side.
The fifth answer is also true because it is just a multiplication of the second and fourth inequalities.
Answer three should be the one that is not true, and we can verify this result with an example: an isosceles triangle with a = 3, b= 3, c= 10 will not satisfy the inequality.
