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

Let the side length of the equilateral triangle be $x$.The area ($a$) is given by:
$$a=\frac{\sqrt{3}}{4}{x}^2$$
The height ($b$) is given by:
$$b=\frac{\sqrt{3}}{2}x$$
Now square the height ($b^2$):
$$b^2={\left(\frac{\sqrt{3}}{2}x\right)}^2=\frac{3}{4}{x}^2$$
Find the ratio $\frac{b^2}{a}$:
$$\frac{b^2}{a}=\frac{\frac{3}{4}{x}^2}{\frac{\sqrt{3}}{4}{x}^2}=\frac{3}{\sqrt{3}}=\sqrt{3}$$