Question : The ratio of inradius and circumradius of an equilateral triangle is:

Option 1: $1:2$

Option 2: $2:1$

Option 3: $1:\sqrt2$

Option 4: $\sqrt2:1$

Question : The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^2$. Find the side (in cm) of the triangle.

Option 1: $2$

Option 2: $4$

Option 3: $\sqrt{3}$

Option 4: $2 \sqrt{3}$

Question : ABCD is a square. Draw an equilateral $\triangle $PBC on side BC considering BC is a base and an equilateral $\triangle $QAC on diagonal AC considering AC is a base. Find the value of $\frac{\text{area of $\triangle PBC$}}{\text{area of $\triangle QAC$}}$.

Option 1: $\frac{1}{2}$

Option 2: $1$

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

Option 4: $\frac{1}{4}$

Question : If the area of an equilateral triangle is $a$ and height $b$, then the value of $\frac{b^2}{a}$ is:

Option 1: $3$

Option 2: $\frac{1}{3}$

Option 3: $\sqrt3$

Option 4: $\frac{1}{\sqrt3}$

Question : If the numerical values of the height and the area of an equilateral triangle are the same, then the length of each side of the triangle is:

Option 1: 2 units

Option 2: 4 units

Option 3: 5 units

Option 4: 8 units