Question

Area of an equilateral triangle is 27 root 3cm square then perimeter is

Answer 1

let the side of the triangle be x
acc. to que.
$\sqrt{3} \div 4x {}^{2} = 27 \sqrt{3} \\ {x}^{2} = 27 \sqrt{3} \times 4 \div \sqrt{3} \\ {x}^{2} = 27 \times 4 \\ x = \sqrt{27 \times 4 } \\ x = \sqrt{3 \times 3 \times 3 \times 2 \times 2} \\ x = 3 \times 2 \sqrt{3} \\ x = 6 \sqrt{3}$
the perimeter of the equilateral triangle =3×s
$3 \times 6 \sqrt{3} \\ 18 \sqrt{3}$
therefore the perimeter of the equilateral triangle is 18root3