Question

If the area of an equilateral triangle is 9√3cm²,then find its perimeter​

Answer 1

Step-by-step explanation:

since:

area of equilateral triangle is √3/4 a^2

and area of triangle =9√3 cm^2 (given)

therefore:

9√3=√3/4 a^2

36cm=a^2

√36=a

6cm = a

therefore the side of triangle is 6cm

hence the perimeter of triangle will be 3×6

=18cm

Answer 2

Given:-

☆Area of an equilateral triangle:-

$= > 9 \sqrt{3} {cm}^{2}$

To find:-

☆Perimeter of the triangle

Solution:-

We know that area of an equilateral triangle is:-

$= > \frac{ \sqrt{ 3} {a}^{2} }{4} sq.units$

Where 'a' is side of the triangle

$= > \frac{ \sqrt{3} {a}^{2} }{4} = 9 \sqrt{3}$

$= > {a}^{2} = \frac{4 \times 9 \sqrt{3} }{ \sqrt{3} }$

$= > {a}^{2} = 36$

$= > a = \sqrt{36}$

$= > a = 6cm$

Since,it is an equilateral triangle,thus all sides of the triangle will be equal.

Thus,the sides of the triangle are 6cm each.

______________________________________

Now,perimeter of a triangle=sum of 3 sides

=>(6+6+6)cm

=>18cm

Thus,perimeter of the equilateral triangle is 18cm.

_______________________________________