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 : 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 : 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 : If each side of an equilateral triangle is 12 cm, then its altitude is equal to:

Option 1: $6 \sqrt{3}\ \text{cm}$

Option 2: $3 \sqrt{6}\ \text{cm}$

Option 3: $6 \sqrt{2}\ \text{cm}$

Option 4: $3 \sqrt{2}\ \text{cm}$

Question : The area of an equilateral triangle is 173.2 cm². Its side will be __________.

Option 1: 20 cm

Option 2: 22 cm

Option 3: 17.32 cm

Option 4: 21.32 cm