The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides of the triangle (in units) are

In $$\triangle A B C$$ with usual notation, $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$ and $$a=\frac{1}{\sqrt{6}}$$, then the area of triangle is _______ sq. units.

Angles of a triangle are in the ratio $$4: 1: 1$$. Then the ratio of its greatest side to its perimeter is

The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the length of the sides of the triangle (in units) are