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 \[\Delta \,AOC\] \[\Rightarrow \] \[6=\frac{1}{2}\times AB\times 2+\frac{1}{2}\times BC\times 2+\frac{1}{2}\times CA\times 2\] \[\Rightarrow \] \[AB+BC+CA=6\,cm\]