Question

If the area of an equilateral triangle is 36√3 cm^2 find the height​

Answer 1

Given:-

• Area of the Equilateral Triangle = 36√3cm²

To Find:-

• Height of an equilateral triangle.

Formula Used:-

• ${\boxed{\bf{Area\:of\: Equilateral\: Triangle=\dfrac{\sqrt{3}}{4}a^2}}}$

• ${\boxed{\bf{Height\:of\: Equilateral\:Triangle=\dfrac{\sqrt{3}}{2}a}}}$

Solution:-

Firstly,

$\sf :\implies\:Area=\dfrac{\sqrt{3}}{4}a^2$

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

$\sf :\implies\:a^2=36\times4$

$\sf :\implies\:a^2=144$

$\sf :\implies\:a=\sqrt{144}$

$\bf :\implies\:a=12\:cm$

Now,

$\sf :\implies\: Height=\dfrac{\sqrt{3}}{2}a$

$\sf :\implies\: Height=\dfrac{\sqrt{3}}{2}\times12$

$\bf :\implies\: Height=6\sqrt{3}\:cm$

Hence, The Height of the Equilateral triangle is 6√3 cm.

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