Question

Area of a equilateral triangle is 24root 3 cm what is perimeter of the equilateral

Answer 1

➡HERE IS YOUR ANSWER⬇

Let, each side of the equilateral triangle is a cm.

Then, the area of the triangle (β)

$= \frac{ \sqrt{3} }{4} \times {a}^{2} \: \: {cm}^{2}$

Given that,

$\beta = 24 \sqrt{3} \: \: \: {cm}^{2}$

So,

$\frac{ \sqrt{3} }{4} {a}^{2} = 24 \sqrt{3} \\ \\ or \: \: {a}^{2} = 96 \\ \\ or \: \: (a - 4 \sqrt{6} )(a + 4 \sqrt{6} ) = 0 \\ \\ since \: \: length \: \: can \: \: not \: \: be \\ negative \\ \\ a = 4 \sqrt{6} \: \: cm$

Hence, the perimeter of the equilateral triangle is
$= 3 \times a \: \: \: cm \\ \\ = 3 \times 4 \sqrt{6} \: \: \: cm \\ \\ = 12 \sqrt{6} \: \: \: cm$

⬆HOPE THIS HELPS YOU⬅