In a triangle ABC if a: b: c= 4:5:6 then ratio between its circumradius and inredius isA. `16/7`B. `16/9`C. `7/16`D. `11/7`

In a triangle ABC if a: b: c= 4:5:6 then ratio between its circumradiu

1.	In a triangle ABC if a: b: c= 4:5:6 then ratio between its circumradius and inredius isA. `16/7`B. `16/9`C. `7/16`D. `11/7`
Answer» `R/r=(abc)/(4Delta)//Delta/s=((abc)s)/(4Delta^2 )rArrR/r=(abc)/(4(s-a)(s-b)(s-c)).....(i)` `therefore a:b:c=4 : 5:6 rArr a/4=b/5=c/6=k`(say) `rArr a=4k,b=5k , c=6k ` `therefore s=(a+b+c)/(2)=(15k)/(2),s-a=(7k)/(2).s-b=(5k)/(2), s-c =(3k)/(2)` using (i) these values `R/r=((4k)(5k)(6k))/(4((7k)/2)((5k)/(2))((3k)/2))=16/7`