Answer:
Option D
Explanation:
We have,
a:b:c =2:3:4
Let a=2k,b=3k, c=4k
$\therefore$ $R= \frac{abc}{4\triangle}$ and $r=\frac{\triangle}{s}$
$\therefore$ $\frac{R}{r}= \frac{s.abc}{4\triangle^{2}} $
$\Rightarrow$ $\frac{R}{r}= \frac{s.(2k)(3k)(4k)}{4s(s-2k)(s-3k)(s-4k)} $
$\Rightarrow$ $\frac{R}{r}= \frac{6k^{3}}{\left(\frac{9k}{2}-2k\right)\left(\frac{9k}{2}-3k\right)\left(\frac{9k}{2}-4k\right)} $
$\left[ \because s=\frac{a+b+c}{2}\right]$
$\frac{R}{r}= \frac{6.2^{3}.k^{3}}{5k.3k.k} \Rightarrow\frac{R}{r}=\frac{16}{5}$
R:r= 16:5
