If $a=2 b=8 c$ and $a+b+c=13$ then the value of $\frac{\sqrt{a^2+b^2+c^2}}{2 c}$ is:

$\frac{9}{2}$

If $a=2 b=8 c$-----(A)

$a+b+c=13$

From equation A the ratio of a : b : c = 8 : 4 : 1

8x + 4x + 1x = 13

13x = 13

x = 1

Then the values of a = 8, b = 4 and c = 1

The value of $\frac{\sqrt{a^2+b^2+c^2}}{2 c}$ = $\frac{\sqrt{8^2+4^2+1^2}}{2 × 1}$

The value of $\frac{\sqrt{a^2+b^2+c^2}}{2 c}$ = $\frac{\sqrt{81}}{2}$ = $\frac{9}{2}$