SOLUTION —
$\begin{array}{l}\text { Now, } \quad \frac{a}{h}=\frac{h}{b}=\frac{g}{f} \\\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}=\frac{-3 / 2}{-3 \sqrt{3} / 2} \Rightarrow \frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{array}$
Which is true hence lines are parallel.
$\therefore \quad d=2 \sqrt{\frac{g^2-a c}{a(a+b)}}=2 \sqrt{\frac{\frac{9}{4}+4}{4}}=\frac{5}{2}$
So, The correct option will be (A).
