In triangle `A B C ,a : b : c=4:5: 6.`The ratio of the radius of the c – InterviewSolution

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1.	In triangle `A B C ,a : b : c=4:5: 6.`The ratio of the radius of the circumcircle to that of the incircleis____.
Answer» Correct Answer - `(16)/(7)` We, have, `R=(abc)/(4Delta)" and "r=Delta/s` `=(abc)/(4(s-a)(s-b)(s-c))` But `a : b : c=4 : 5 : 6" "["given"]` `rArr" "a/4=b/5=c/6=k" [let]"` `rArr" "a=4k, b=5k, c=6k` `"Now, "s=1/2(a+b+c)=1/2(4k+5k+6x)=(15k)/2` `:." "R/r=((4k)(5k)(6k))/(4((15k)/2-4k)((15k)/2-5k)((15k)/2-6k))` `=(30k^(3))/(k^(3)((15-8)/2)((15-10)/2)((15-12)/2))=(30.8)/(753)=16/7`

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