Question

If `(3a+5b):(3a-5b): :(3c+5d):(3c-5d)`, then show that a,b,c and d are in proportion.

Answer 1

Given `(3a+5b)/(3a-5b)=(3c+5d)/(3c-5d)` ltbRgt Using componendo and dividendo rule
`implies((3a+5b)+(3a-5b))/((3a+5b)-(3a-5b))=((3c+5d)+(3c-5d))/((3c+5d)-(3c-5d))`
`implies(6a)/(10b)=(6c)/(10d)implies(a)/(b)=(c)/(d)`
`thereforea,b,c and d` are in proportion.