Question

If the area of an equilateral triangle is 16√3 cm2 , then the perimeter of the triangle is

Answer 1

answer is 24 cm thanks

Answer 2

$\boxed{Here's\: your\: solution}$

We know that,

Area of equilateral triangle = √3/4 × side²

=> Area = √3/4 s²

But, according to the question,

Area = 16√3 cm²

Hence, both areas are equal

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

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

$= > {a}^{2} = 16 \times 4$

$= > {a}^{2} = 64$

$= > a = \sqrt{64}$

$= > a = \sqrt{8 \times 8}$

$= > a = 8$

Hence, one side of the triangle is 8 cm

Now, we know that sides of equilateral triangle are equal, i.e., a=b=c

Then, Perimeter
= sum of all sides
= a + b +c
= a + a + a (a=b=c)
= 3a
= 3 × 8
= 24 cm

$\boxed{\pink{Hence, \: your \: answer \: is \: 24\: cm}}$

Hope this answer helps you..