Question

if the area of an equilateral triangle is 36 root 3 cm square find its height

Answer 1

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First of all let us calculate the side of this equilateral triangle.

Let the sides of equilateral triangle be "s" cm.

Also, Area of equilateral triangle = √3/4×(s)²

Then, √3/4 × (s)² = 36√3

=> s²/4 = 36

=> (s/2)² = 36

=> s/2 = √36 cm or 6 cm.

=> s = (6×2) cm = 12 cm.

Now, by using the formula, we get :

Height of equilateral triangle

= √3/2 × (s)

= √3/2 × (12)

= 6√3 cm.

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Answer 2

Height of the triangle = 6√3 cm

Given:

The area of an equilateral triangle = 36√3 cm²

To find:

Find height of triangle

Solution:

Given area of triangle = 36√3

As we know area of equilateral triangle A = √3a²/4

Where a is equal side of triangle  

From given data √3a²/4 = 36√3

⇒ a²/4 = 36

⇒ a² = 144

⇒ a² = 12²  

Therefore, equal side of triangle = 12 cm  

The formula for height of equilateral, h = √3a/2

= √3(12)/2 = √3(6) = 6√3 cm

Height of the triangle =  6√3 cm  

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