Question

If the area of an equlateral triangle is 8 root of 3.Find the perimeter​

Answer 1

SOLUTION:-

Given:

The area of an equilateral ∆ is 8√3.

We know that, area of an equilateral ∆ is;

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

$= > \frac{ \sqrt{3} }{4} {a}^{2} = 8 \sqrt{3} \\ \\ = > {a}^{2} = 32 \\ \\ = > a = \sqrt{32} \\ \\ = > a = 4 \sqrt{2} cm$

Now,

Perimeter of triangle:

=) 3× side

=) 3 × 4√2

=) 3× 4× 1.414

=) 3× 5.656

=) 16.968cm

Hope it helps ☺️

Answer 2

Correct Question :-

If the area of an equilateral triangle is 8 root of 3 units². Find the perimeter.

Answer :-

Perimeter of an equilateral triangle is 12√2 units.

Explanation :-

Finding the side of equilateral triangle

Given

Area of an equilateral triangle = 8√3 units²

Also

Area of an equilateral triangle = (√3/4) * a²

[Where a = side of an equilateral triangle]

⇒ 8√3 = (√3/4) * a²

⇒ 8√3 * 4 = a²

⇒ 32√3 = √3a²

⇒ 32√3/√3 = a²

⇒ 32 = a²

⇒ √32 = a

⇒ √16 * √2 = a

⇒ 4 * 1.414 = a

[ ∵ √2 = 1.414]

⇒ 5.616 = a

⇒ a = 5.616

Side of an equilateral triangle = 5.616 units

Finding perimeter of an equilateral triangle

Perimeter of an eqilateral triangle = 3a

= 3 * 5.616

= 16.968

∴ perimeter of an equilateral triangle is 16.968 units.