Properties of Triangles question bank (Maths)

In $\mathrm{\Delta ABC},$ the lengths of sides $AC$ and $AB$ are $12 \mathrm{cm}$ and $5 \mathrm{cm},$ respectively. If the area of $∆\mathrm{ABC}$ is $30{ \mathrm{cm}}^2$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $\mathrm{\Delta ABC}$, then the value of $2R+r \left(\text{in cm}\right)$ is equal to ______ .

The lengths of two adjacent sides of a cyclic quadrilateral are $2$ units and $5$ units and the angle between them is ${60}^{\mathrm{o}}$. If the area of the quadrilateral is $4\sqrt{3}$ sq. units, then the perimeter of the quadrilateral is