Question

If perimeter of an equilateral triangle is equal to its area. Find the area of the
equilateral triangle ?​

Answer 1

Answer:

Let the side of the equilateral triangle be a.

Hence, Its perimeter = 3a

and area will be = √3/4 × a²

So, as perimeter = Area

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

$= > \frac{ \sqrt{3} }{4} a = 3$

$= > a = \frac{12}{ \sqrt{3} }$

$= > a = 4 \sqrt{3}$

Hence, area will be:

$\frac{ \sqrt{3} }{4} \times 4 \sqrt{3} \times 4 \sqrt{3}$

$= 12 \sqrt{3}$

and that is the answer

Answer 2

Answer:

let side of the equilateral triangle be a

perimeter of the =a+a+a=3a

area of equilateral =(3^1/2 )/4 *a*a

3a=(3^1/2)/4 *a*a

a=4*3^1/2

area=√3/4 *4*√3 *4*√3

=12√3