SSC CGL Tier II 21 Sep 2014 Paper

(1) Lateral surface area of prism = 3 × side × height
∴ 3 × side × height = 120
⇒ Side × height = $\frac{120}{3}$= 40 sq.cm. ...(i)
Volume of prism = Area of base × height
$\Rightarrow 40\sqrt{3}=\frac{\sqrt{3}}{4}\times$ side ${}_{}^2\times$ height
$\Rightarrow \frac{40\sqrt{3}\times 4}{\sqrt{3}}={\mathrm{side}}^2\times$ height
$\Rightarrow {\mathrm{side}}^2\times$ height
= 160 cu.cm ...(ii)
Dividing equation (ii) by (i),
Side $=\frac{160}{40}=4\mathit{c}\mathit{m}$