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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Question : The median of an equilateral triangle is $15 \sqrt{3} \mathrm{~cm}$. What is the side of this triangle?
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Question : $\triangle \mathrm{MNO}$ is similar to $\triangle \mathrm{STU}$. Perimeters of $\triangle \mathrm{MNO}$ and $\triangle \mathrm{STU}$ are 80 cm and 200 cm respectively. If ON = 25 cm, then what is the length of TU?
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