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An equilateral triangular sheet is formed by joining 9 equilateral triangular sheets each of area \(9\sqrt 3 \) cm2. What is the height of the bigger triangular sheet?

An equilateral triangular sheet is formed by joining 9 equilateral triangular sheets each of area \(9\sqrt 3 \) cm2. What is the height of the bigger triangular sheet? Correct Answer <span class="math-tex">\(9\sqrt 3 \,{\rm{cm}}\)</span>

Given:

Area of each smaller equilateral triangle = 9√3 cm2

Concept Used:

Area of equilateral triangle = √3a2/4

Height of equilateral triangle = √3a/2 

Where, a = side of the equilateral triangle 

Calculation:

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Let the side length of each smaller triangle be a cm 

Since the area of each smaller equilateral triangle = 9√3 cm2

So, √3a2/4 = 9√3

⇒ a = 6 cm 

So, the side of bigger equilateral triangle ABC = 6 × 3 = 18 cm 

So, Height AD of the bigger equilateral triangle = (√3 × 18)/2 = 9√3 cm

∴ The required height of the bigger equilateral triangle is 9√3 cm.

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