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 : $ABC$ is a right-angled triangle, right-angled at B and $\angle A=60°$ and $AB=20$ cm, then the ratio of sides $BC$ and $CA$ is:

Option 1: $\sqrt{3}:1$

Option 2:

$1:\sqrt{3}$

Option 3:

$\sqrt{3}:\sqrt{2}$

Option 4:

$\sqrt{3}:2$

Question : The sides of a triangle are 20 cm, 21 cm, and 29 cm. The area of the triangle formed by joining the midpoints of the sides of the triangle will be:

Option 1: $67 \frac{2}{3}$ cm²

Option 2: $52 \frac{1}{2}$ cm²

Option 3: $47 \frac{1}{2}$ cm²

Option 4: $58 \frac{1}{3}$ cm²

Question : If $\triangle ABC$~$\triangle PQR$, the ratio of perimeter of $\triangle ABC$ to perimeter of $\triangle PQR$ is 36 : 23 and QR = 3.8 cm, then the length of BC is:

Option 1: $4 \frac{103}{121} cm$

Option 2: $3 \frac{109}{121} cm$

Option 3: $5 \frac{109}{115} cm$

Option 4: $3 \frac{107}{115} cm$

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