Mathematics - Properties of Triangle Question with Solution | TestHub

$\tan \frac{B}{2}=\frac{2}{3}\cdot \tan \frac{C}{2}=\frac{1}{2}\Rightarrow \tan \frac{A}{2}=\frac{4}{7}$

$\tan \frac{B}{2}\cdot \tan \frac{C}{2}=\frac{s-a}{s}\Rightarrow 2s=3a=42$

∴ Perimeter $=42$

$\therefore \Delta =$ r.s. $=84{\mathrm{cm}}^2$

$\therefore \tan \frac{A}{2},\tan \frac{B}{2},\tan \frac{C}{2}$ all are less than 1. All angles are acute.