Question

Find the perimeter of an equilateral triangle whose area is `16sqrt(3)"cm"`.

Answer 1

We know that, Area of an equilateral triangle(A) of side a is

A = `sqrt(3)/(4)"a"^2`

Here, A = `16sqrt(3)`

⇒ `16sqrt(3) = (sqrt(3))/(4)"a"^2`

⇒ 16 = `"a"^2/(4)`

⇒  4 x 16 = a²
⇒ a
= 2 x 4 
= 8
i.e. side of the equilateral triangle is 8cm
The perimeter of an equilateral triangle of side a = 3a
⇒ The Perimeter of an equilateral triangle of side 8cm
= 3 x 8
= 24cm.