In a $\Delta ABC,$ if $a = 2x,$ $b = 2y$ and $\angle C = 120^\circ,$ then the area of the triangle is

In a $\Delta ABC,$ if $A:B:C = 3:5:4,$ then $a + b + c\sqrt{2}$ is equal to

If two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^{\circ}$. If the third side is $3$,then the remaining fourth side is :-

In $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then $a+c : b =$

In a triangle $ABC$,$b = \sqrt{3}$,$c = 1$ and $\angle A = 30^\circ$,then the largest angle of the triangle is ....$^\circ$

If $p_1, p_2, p_3$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and if $\Delta$ is the area of the triangle,$S$ is the semi-perimeter of the triangle,then find the value of $\frac{\cos A}{p_1} + \frac{\cos B}{p_2} + \frac{\cos C}{p_3}$.