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Thread: Triangle Inequality

  1. #1
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    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:
    Triangle Inequality-socrates.png

    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.
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  2. #2
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    Re: Triangle Inequality

    Quote Originally Posted by socrateszeno View Post
    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:
    Click image for larger version. 

Name:	socrates.png 
Views:	2 
Size:	4.7 KB 
ID:	38473

    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?
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