# Thread: Triangle Inequality

1. ## Triangle Inequality

ABC is a triangle.
m(CAB) = α degrees
m(BCA)=θ degrees
α+θ>90 degrees
α>θ
|BC|=8 units
What can be the maximum integer value of perimeter of ABC ?

My work:

Angle B is obtuse angle.
AB<8
AB+AC>8
Let AB be 7.8,Let AC be 7.9
AB+BC+AC=23.7
But the answer is 27.

2. ## Re: Triangle Inequality

Originally Posted by socrateszeno
ABC is a triangle.
m(CAB) = α degrees
m(BCA)=θ degrees
α+θ>90 degrees
α>θ
|BC|=8 units
What can be the maximum integer value of perimeter of ABC ?

My work:

Angle B is obtuse angle.
AB<8
AB+AC>8
Let AB be 7.8,Let AC be 7.9
AB+BC+AC=23.7
But the answer is 27.
If the sum of two angles is greater than 90, then the third angle must be less than 90.

How do you conclude that B is obtuse?