Question

Hii friends.
Please answer me this question...

Answer 1

We know that area of an equilateral triangle = √3/4 × side²
=> Area = √3/4 a²

But, According to question,
area = 32√3

Hence, both areas are equal

$= > \frac{ \sqrt{3} }{4} {a}^{2} = 32 \sqrt{3}$

$= > {a}^{2} = \frac{32 \sqrt{3 } \times 4 }{ \sqrt{3} }$

$= > {a}^{2} = 32 \times 4$

$= > {a}^{2} = 128$
$= > a = \sqrt{128}$
$= > a = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}$
$= > a = 2 \times 2 \times 2 \sqrt{2}$
$= > a = 8 \sqrt{2}$
$= > a = 11.3 \:( approx)$

Now, since all sides are equal in an equilateral triangle,

a + b + c
= a + a + a
= 3a
= 3 × 11.3
= 33.9 cm.

$\boxed{\purple{Hence, \: the\: perimeter\: is \: 33.9\: cm}}$