Question

The perimeter of an equilateral triangle is
$\sqrt{3 } \: times$
it's area. Find the length of each side.

Answer 1

Mensuration,

Let the sides of the equilateral triangle as a

So it's perimeter is 3a

So its are is = 3√3a

But we know that the area of equilateral triangle as ,area = √3/4×a² [ where a is the length of each sides]

ATQ,
3√3a = √3/4 × a²
=> a = 12 units

So the lenght of each side is 12 units

That's it
Hope it helped (´°̥̥̥̥̥̥̥̥ω°̥̥̥̥̥̥̥̥｀)

Answer 2

look here is it

Let the sides of the equilateral triangle as @

So it's perimeter is 3@

So its are is = 3√3@

But we know that the area of equilateral triangle as ,area = √3/4×@² [ where @ is the length of each sides]

ATQ,
3√3@ = √3/4 × a²
=>@a = 12 units

lenght of each side is 12 units