Choose the correct answer of the following question:

Let the base of the triangle be $3 x$ and its height be $4 x$.

As, the area of the triangle $=216 \mathrm{~cm}^{2}$

$\Rightarrow \frac{1}{2} \times$ Base $\times$ Height $=216$

$\Rightarrow \frac{1}{2} \times 3 x \times 4 x=216$

$\Rightarrow 6 x^{2}=216$

$\Rightarrow x^{2}=\frac{216}{6}$

$\Rightarrow x^{2}=36$

$\Rightarrow x=\sqrt{36}$

$\Rightarrow x=6 \mathrm{~cm}$

So, the height of the triangle $=4 \times 6=24 \mathrm{~cm}$

Hence, the correct answer is option (b).