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A box in the shape of a right triangular prism is made using two equilateral triangles, the perimeter of each equilateral triangle is 24√3 cm and the total surface area of the box is 336√3 cm2, then what is the height of the box?


1. 15 cm
2. 10 cm
3. 12 cm
4. 13 cm

1 Answer

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Best answer
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

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