Question

the area of equilateral triangle is
$16 \sqrt{3}$
find its perimeter​

Answer 1

so area of equilateral triangle $\frac{\sqrt{3}}{4}×a^2$

$\frac{\sqrt{3}}{4}×a^2 = 16 \sqrt{3}$

on cancelling $\sqrt{3}$

$\frac{1}{4}×a^2 = 16$

$a^2 = 16×4$

$a = \sqrt{16×4}$

$a = 8$

$perimeter=8×3$

$perimeter=24 cm$

Answer 2

The area of a equilateral triangle = 16√3

We know that,

The area of equilateral triangle = $\bf \frac{\sqrt{3}}{4}a^{2}$

[ in which 'a' is the 'side' of the triangle ]

$\bf \frac{\sqrt{3}}{4}a^{2} = 16\sqrt{3}\\\\a^{2}=16\sqrt{3}\times\frac{4}{\sqrt{3}}\\\\a^{2}=64\\\\a=\sqrt{64}\\\\a=8$

So,

each side of equilateral triangle = 8

perimeter = sum of all sides

= 8+8+8

= 24