Question

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

Answer 1

$\Delta=\frac{1}{2} \cdot 5.12 \cdot \sin A =30$
$\sin A =1$
$A =90^{\circ} \Rightarrow BC =13$
$BC =2 R =13$
$r =\frac{\Delta}{ S }=\frac{30}{15}=2$
$2 R + r =15$