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

Solution (By Examveda Team)

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