Night reader wrote:If a, b and c are the sides of any triangle, which of the following inequalities is not true?
A. ab > 0
B. a + b > c
C. a + c/2 >b
D. b + c > a
E. (a + b)*(b + c) > a*c
I came up with E after canceling A...D
Patiently attack this problem. If you have 2 minutes, use them properly.
We dont/can't have negative sides of the triangle, so A is true
B is true because in any triangle sum of 2 sides is greater than the third side
C: a + c/2 >b
2a + c> 2b
2a-2b > c
2b - 2a < c
There is no rule that verifies this statement. False
d. Same as B.
e. Multiply it out:
ab + ac + b^2 + bc> ac
ac cancels out from both side of the equation
b(a + b + c) >0
since b is greater than 0 (positive side), we have
a +b+c > 0, which is true
