Multiple Choice Question (MCQ)
If a, b,c are 3 side of △ABC中 such that (b+c):(c+a):(a+b) = 4:5:6, then the maximum internal angle of △ABC is

×
90\degree

×
150\degree

✓
120\degree

×
75\degree
If a, b,c are 3 side of △ABC中 such that (b+c):(c+a):(a+b) = 4:5:6, then the maximum internal angle of △ABC is
90\degree
150\degree
120\degree
75\degree
Let
Addition of the three equations
2(a+b+c)=15k, that is,
Substituting (1),(2), (3) to (4) gives
a=3.5k,b=2.5k,c=1.5k
Therefore, the maximum internal angle is A,
Using the law of cosine：
\cos A = \dfrac{b^2+c^2a^2}{2bc}
=\dfrac{6.25k^2+2.25k^212.25k^2}{7.5k^2}
=1
\because A∈(0, 180°)
\therefore A=120°．
Therefore, the maximum internal angle of △ABC is 120°
Option C is the right choice.