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 : The altitude of an equilateral triangle of side $\frac{2}{\sqrt3}$ cm is:

Option 1: $\frac{4}{3}$ cm

Option 2: $\frac{4}{\sqrt3}$ cm

Option 3: $\frac{2}{3}$ cm 

Option 4: $1$ cm

Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

Option 1: 6

Option 2: 5

Option 3: 4.5

Option 4: 12

Question : In $\triangle$ABC, $\angle$C = 90° and CD is perpendicular to AB at D. If $\frac{\text{AD}}{\text{BD}}=\sqrt{k}$, then $\frac{\text{AC}}{\text{BC}}$=?

Option 1: $\sqrt{k}$

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

Option 3: $\sqrt[4]{k}$

Option 4: $k$

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: $2 \sqrt{3}$