The base of a right prism is an equilateral triangle. If the lateral surface area and volume are 120 cm2, 40√3 cm3 respectively then the side of base of the prism is

Answer: Option A

Lateral surface area of prism = 120
Base perimeter × height = 120
3 × (side) × height = 120
(Perimeter of equilateral Δ = 3 × side)
Side × height = $$\frac{120}{3}$$  = 40 . . . . . (i)
Volume of prism = 40√3
Area of base × height = 40√3
$$\frac{\sqrt{3}}{4}$$ (side)² × height = 40√3
(side)² × height = $$=\frac{40\sqrt{3}\times 4}{\sqrt{3}}$$   = 160 . . . . . (ii)
Dividing equation (ii) by equation (i)
$$\frac{{\left(\text{side}\right)}^2\times \text{height}}{\text{side}\times \text{height}}=\frac{160}{40}$$
side = 4 cm