Question

If the area of an equilateral triangle is 81 root under 3 cm square find its height

Answer 1

Heya

∆ Given the side of an Equilateral Triangle : A

∆ Height :
$\frac{ \sqrt{3} }{2} a$

And Area :

$\frac{ \sqrt{3} }{4} {a}^{2}$

Hence, Equating the Formula and solving :

$\frac{ \sqrt{3} }{4} {a}^{2} = 81 \sqrt{3}$

$= > {a}^{2} = {(9 \times 2)}^{2}$

$= > a = 18cm$

$= > \frac{ \sqrt{3} }{2} a = 9 \sqrt{3}$

And hence, the height of the Triangle is :

$9 \sqrt{3} cm$