Question : In an equilateral triangle STU, inradius is $5 \sqrt{3 }\mathrm{~cm}$. What is the length of the side of this equilateral triangle?
Option 1: $20 \sqrt{3} \mathrm{~cm}$
Option 2: $18 \sqrt{3} \mathrm{~cm}$
Option 3: $30 \mathrm{~cm}$
Option 4: $24 \mathrm{~cm}$
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Correct Answer: $30 \mathrm{~cm}$
Solution :
In an equilateral triangle, the inradius (r) is related to the side length ($a$) by,
$ a = 2\sqrt{3}r $
Given that the inradius, $r=5\sqrt{3}$ cm,
$⇒a = 2\sqrt{3} \times 5\sqrt{3} = 2 \times 15 = 30 \text{ cm} $
Hence, the correct answer is $30 \mathrm{~cm}$.
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