If $r_1,r_2,r_3$  are in H.P if the area of a triangle is 24 and perimeter is also 24. Then if the length of its largest side is $k$ then $\frac{k}{5}$   is equal to

$$\begin{gathered} \Delta =24,s=12,r=\frac{\Delta }{s}=2;r_1,r_2,r_3 are in H.P \\ \Rightarrow \frac{2}{r_2}=\frac{1}{r_1}+\frac{1}{r_3}\Rightarrow \frac{3}{r_2}=\frac{1}{r}\Rightarrow r_2=6 \\ r.r_1.r_2.r_3={\Delta }^2 \Rightarrow r_1{r}_3=48\Rightarrow \frac{2}{r_2}=\frac{1}{r_3}+\frac{1}{r_1}\Rightarrow \frac{1}{r_3}+\frac{1}{r_1}=\frac{1}{3}\Rightarrow r_3+r_1=16 \\ {r}_1=12,r_3=4\Rightarrow r_1:r_2:r_3=6:3:2 a:b:c=10:8:6 \end{gathered}$$

Largest side is 10