If the area of the base, height and volume of a right prism be $\left(\frac{3 \sqrt{3}}{2}\right) \mathrm{P}^{2} \mathrm{~cm}^{2}, 100 \sqrt{3} \mathrm{~cm}$ and $7200 \mathrm{~cm}^{3}$ respectively, then the value of $\mathrm{P}$ will be

Volume of prism = Area of base × height

$\Rightarrow 7200=\frac{3 \sqrt{3}}{2} \mathrm{P}^{2} \times 100 \sqrt{3}$

$\Rightarrow 7200=50 \times 3 \times 3 \mathrm{P}^{2}$

$\Rightarrow \mathrm{P}^{2}=\frac{7200}{50 \times 3 \times 3}=16$

$\Rightarrow \mathrm{P}=\sqrt{16}=4$