Correct Answer - Option 2 : 10 cm
Given:
The perimeter of the triangle = 24√3 cm
The total surface area of the box = 336√3 cm2
Formula used:
The area of the equilateral triangle = (√3/4) × (side)2
The perimeter of an equilateral triangle = 3 × side
The total surface area of the prism = 2(Area bases) + Height of prism × Perimeter of base
Calculation:
Let the height of the box be h cm
Side of the equilateral triangle = perimeter/3
⇒ 24√3/3 = 8√3
The area of base of the box = (√3/4) × (side)2
⇒ (√3/4) × (8√3)2
⇒ 48√3 cm2
The total surface area of prism = 2(Area bases) + Height of prism × Perimeter of base
⇒ 96√3 + h × 24√3 = 336√3
⇒ h × 24√3 = 240√3
⇒ h = 10
∴ The height of the box is 10 cm