Problem Solving

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

C

Why E is not true? If u take sides 3,4,5, then (3+4) * (4+5) is > 3* 5

N:Dure wrote:C

Why E is not true? If u take sides 3,4,5, then (3+4) * (4+5) is > 3* 5

you are correct OA is C too

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

c

imagine a=3, c=4, b=5