Question : The inradius of an equilateral triangle is $\sqrt3$ cm, then the perimeter of that triangle is:
Option 1: 18 cm
Option 2: 15 cm
Option 3: 12 cm
Option 4: 6 cm
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Correct Answer: 18 cm
Solution :
Given, the inradius of an equilateral triangle is $\sqrt3$ cm.
We know, In-radius of equilateral triangle = $\frac{\text{side}}{2\sqrt3}$
⇒ $\sqrt3=\frac{\text{side}}{2\sqrt3}$
⇒ side = $\sqrt3\times2\sqrt3$
$\therefore$ side = $2\times 3$ = 6 cm
Now, perimeter = 3$\times$ (side) = $3\times 6$ = 18 cm
Hence, the correct answer is 18 cm.
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