Question : The radius of the incircle of a triangle is 2 cm. If the area of the triangle is 6 cm2, then its perimeter is:
Option 1: 2 cm
Option 2: 3 cm
Option 3: 6 cm
Option 4: 9 cm
Correct Answer: 6 cm
Solution :
Since the radius of the incircle is 2 cm.
$\therefore$ OD = OE = OF = 2 cm
$\therefore$ Area of $\triangle$ABC = Area of $\triangle$AOB + Area of $\triangle$BOC + Area of $\triangle$AOC
⇒ $6 = \frac{1}{2} \times AB \times 2+\frac{1}{2} \times BC \times 2+\frac{1}{2} \times CA \times 2$
⇒ $AB + BC + CA = 6$ cm
$\therefore$ The perimeter of the triangle = 6 cm
Hence, the correct answer is 6 cm.
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