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Find In ratio and proportion, if a:b:c=2:3:5 then find (a^2+b^2+c^2)/(ab+bc+ca)

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Your problem `->` In ratio and proportion, if a:b:c=2:3:5 then find (a^2+b^2+c^2)/(ab+bc+ca)


`a:b:c=2:3:5`

`:.a/2=b/3=c/5`

Let `a/2=b/3=c/5=k` (say)

`:. a/2=k,b/3=k,c/5=k`

`:.a=2k,b=3k,c=5k`

Now `(a^2+b^2+c^2)/(ab+bc+ca)`

`=(4k^2+9k^2+25k^2)/(6k^2+15k^2+10k^2)`

`=(38k^(2))/(31k^(2))`

Cancel the common factor `k^(2)`

`=(38)/(31)`






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