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 : 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 : $\triangle \mathrm {ABC}$ is similar to $\triangle \mathrm{PQR}$ and $\mathrm{PQ}=10 \mathrm{~cm}$. If the area of $\triangle \mathrm{ABC}$ is $32 \mathrm{~cm}^2$ and the area of $\triangle \mathrm{PQR}$ is $50 \mathrm{~cm}^2$, then the length of $A B$ (in $\mathrm{cm}$ ) is equal to:

Option 1: 10

Option 2: 4

Option 3: 6

Option 4: 8

Question : In an equilateral triangle, the circumradius is 14 cm. What is the length of the median in this triangle?

Option 1: $14 \sqrt{3} \mathrm{~cm}$

Option 2: $21 \mathrm{~cm}$

Option 3: $18 \sqrt{3} \mathrm{~cm}$

Option 4: $7 \sqrt{3} \mathrm{~cm}$

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: $24 \mathrm{~cm}$