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Jf A:B =C:D, Then Prove that (A2 + C2)/(B2 + D2) = (Ac)/(Bc) - ICSE Class 10 - Mathematics

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Question

If a : b =c : d, then prove that `("a"^2 + "c"^2)/("b"^2 + "d"^2) = ("ac")/("bc")`

Solution

`"a"/"b" = "c"/"d" => "a" = "bc"/"d"`

To prove, 

`("a"^2 + "c"^2)/("b"^2 + "d"^2) = ("ac")/("bd")`

LHS

`("a"^2 + "c"^2)/("b"^2 + "d"^2) `

`=(("bc"/"d")^2 + "c"^2)/("b"^2 + "d"^2)`

`= (("b"^2"c"^2)/"d"^2 + "c"^2)/("b"^2 + "d"^2)`

`= ("c"^2 ("b"^2 + "d"^2))/("d"^2("b"^2 + "d"^2))`

`= "c"^2/"d"^2`

RHS

`("ac")/("bd")`

`= (("bc")/"d" "c")/("bd")`

`="bc"^2/"bd"^2`

`= "c"^2/"d"^2`

LHS = RHS

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 4

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Solution Jf A:B =C:D, Then Prove that (A2 + C2)/(B2 + D2) = (Ac)/(Bc) Concept: Componendo and Dividendo Properties.
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