Question

The height of equilateral triangle having area 36root 3

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Answer 1

Answer:

area of equilateral triangle=√3a²/4=36√3

a²=36×4

a=12

so height=√3a/2

=12√3/2

6√3

Answer 2

Given :

• Area of the equilateral triangle = 36√3 unit².

To find :

The height of the Equilateral triangle.

Solution :

To find the height of the equilateral triangle , first we have to find the radius of the triangle.

Since , we are provided with the area of the triangle , we can use the formula for Area of a equilateral triangle and by Substituting the value of area in it , we can find the required value.

Area of a equilateral triangle :

Formula for area of a equilateral triangle :-

$\boxed{\bf{A = \dfrac{\sqrt{3}\:a^{2}}{4}}}$

• A = Area of the equilateral triangle.

• a = Equal side of the equilateral triangle.

Now using the formula for area of a equilateral triangle and substituting the values in it, we get :

$:\implies \bf{36\sqrt{3} = \dfrac{\sqrt{3}\:a^{2}}{4}}$

By multiplying 4 on both the sides of the equation , we get :

$:\implies \bf{36\sqrt{3} \times 4 = \dfrac{\sqrt{3}\:a^{2}}{4} \times 4}$

$:\implies \bf{36\sqrt{3} \times 4 = \dfrac{\sqrt{3}\:a^{2}}{\not{4}} \times \not{4}}$

$:\implies \bf{144\sqrt{3} = \sqrt{3}\:a^{2}}$

Now by dividing √3 on both the sides, we get :

$:\implies \bf{\dfrac{144\sqrt{3}}{\sqrt{3}} = \dfrac{\sqrt{3}\:a^{2}}{\sqrt{3}}}$

$:\implies \bf{\dfrac{144\not{\sqrt{3}}}{\not{\sqrt{3}}} = \dfrac{\not{\sqrt{3}}\:a^{2}}{\not{\sqrt{3}}}}$

$:\implies \bf{144 = a^{2}}$

By Square rooting on both the sides , we get :

$:\implies \bf{\sqrt{144} = \sqrt{a^{2}}}$

$:\implies \bf{12 = a}$

$\boxed{\therefore \bf{a = 12\:units}}$

Hence, the side of the equilateral triangle is 12 units.

Now ,

To find the height of the equilateral triangle :

We know the formula for height of a equilateral triangle i.e,

$\boxed{\bf{h = \dfrac{\sqrt{3}\:a}{2}}}$

Where :

• h = Height of the equilateral triangle

• a = Equal side of the equilateral triangle.

By using the above formula for height of a equilateral triangle and substituting the values in it, we get :

$:\implies \bf{h = \dfrac{\sqrt{3}\:a}{2}}$

$:\implies \bf{h = \dfrac{\sqrt{3} \times 12}{2}}$

$:\implies \bf{h = \sqrt{3} \times 6}$

$:\implies \bf{h = 6\sqrt{3}}$

$\boxed{\therefore \bf{h = 6\sqrt{3}}}$

Hence the height of the Equilateral triangle is 6√3 units.