question_answer

The radius of the incircle of a triangle is 2 cm. If the area of the triangle is \[6\,c{{m}^{2}},\] then its perimeter is

A) 2 cm                            

B) 3 cm

C) 6 cm                

D) 9 cm

Correct Answer: C

Solution :

            \[OD=OE=OF=2\,cm\] \[\therefore \] Area of \[\Delta \,ABC\] = Area of \[\Delta \,AOB\] + Area of \[\Delta \,BOC\] + Area of \[\Delta \,AOC\] \[\Rightarrow \]   \[6=\frac{1}{2}\times AB\times 2+\frac{1}{2}\times BC\times 2+\frac{1}{2}\times CA\times 2\] \[\Rightarrow \]   \[AB+BC+CA=6\,cm\]