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: $24 \mathrm{~cm}$

Question : The median of an equilateral triangle is $15 \sqrt{3} \mathrm{~cm}$. What is the side of this triangle?

Option 1: 24 cm

Option 2: 18 cm

Option 3: 30 cm

Option 4: 36 cm

Question : Find the area of an equilateral triangle whose sides are 12 cm.

Option 1: $38 \sqrt{3} \mathrm{~cm}^2$

Option 2: $35 \sqrt{3} \mathrm{~cm}^2$

Option 3: $34 \sqrt{3} \mathrm{~cm}^2$

Option 4: $36 \sqrt{3} \mathrm{~cm}^2$

Question : The sides of a triangle are 9 cm, 6 cm, and 5 cm. What is the value of the circumradius of this triangle?

Option 1: $\frac{9 \sqrt{2}}{2} \mathrm{~cm}$

Option 2: $\frac{9 \sqrt{3}}{5} \mathrm{~cm}$

Option 3: $\frac{9 \sqrt{3}}{4} \mathrm{~cm}$

Option 4: $\frac{27 \sqrt{2}}{8} \mathrm{~cm}$

Question : The three sides of a triangle are 7 cm, 9 cm, and 8 cm. What is the area of the triangle?

Option 1: $12 \sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$

Option 2: $10\sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$

Option 3: $12 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$

Option 4: $2 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$