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If (a+3d)/(a+9d)=(a+d)/(a+5d)=k then k...

If `(a+3d)/(a+9d)=(a+d)/(a+5d)=k ` then k is equal to`(a , d >0)`

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When two ratios are equal, then the four quantities compositing them are said to be proportiona. If a/b=c/d, then it is written a:b=c:dor a:b::c:d. Also if a/b=c/d=lamdaimpliesa=blamdaand c=dlamdaimpliesa/b=c/d =(a+-c)/(b+-d)=(""^(n)sqrt((a)^(n)+-(c)^(n)))/(""^(n)sqrt((b)^(n)+-(d)^(n)))=lamda(lamdagt0) important property of proportion : 1. If a:b=c:d,then (a+b)/(b)=(c+d)/(d)("Componendo")i.e.(a)/(b)=(c)/(d)implies(a)/(b)+1=(c)/(d)+1 2. If a:b=c"d, then (a-b)/(b)=(c-d)/(d)("Dividenod")i.e.(a)/(b)=(c)/(d)implies(a)/(b)-1=(c)/(d)-1 3. If a:b:=c:d, then (a+b)/(a-b)=(c+d)/(c-d)("Componendo and dividendo") If ""(a+3d)/(a+9d)=(a+d)/(a+5d)=k, then k is equal to (a,d gt0)

When two ratios are equal, then the four quantities compositing them are said to be proportiona. If a/b=c/d, then it is written a:b=c:dor a:b::c:d. Also if a/b=c/d=lamdaimpliesa=blamdaand c=dlamdaimpliesa/b=c/d =(a+-c)/(b+-d)=(""^(n)sqrt((a)^(n)+-(c)^(n)))/(""^(n)sqrt((b)^(n)+-(d)^(n)))=lamda(lamdagt0) important property of proportion : 1. If a:b=c:d,then (a+b)/(b)=(c+d)/(d)("Componendo")i.e.(a)/(b)=(c)/(d)implies(a)/(b)+1=(c)/(d)+1 2. If a:b=c"d, then (a-b)/(b)=(c-d)/(d)("Dividenod")i.e.(a)/(b)=(c)/(d)implies(a)/(b)-1=(c)/(d)-1 3. If a:b:=c:d, then (a+b)/(a-b)=(c+d)/(c-d)("Componendo and dividendo") If ""(a+3d)/(a+9d)=(a+d)/(a+5d)=k, then k is equal to (a,d gt0)

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