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If (7a + 12b)/(7c + 12d) Then Prove that A/B=C/D - ICSE Class 10 - Mathematics

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Question

If `(7"a" + 12"b")/(7"c" + 12"d")` then prove that `"a"/"b"="c"/"d"`

Solution

`(7"a" + 12"b")/(7"c" + 12"d") = (7"a" - 12"b")/(7"c" - 12"d")`

Applying alternendo, 


`(7"a" + 12"b")/(7"a" - 12"b") = (7"c" + 12"d")/(7"c" - 12"d")`


Applying componendo and dividendo, 


`(7"a" + 12"b" + 7"a" - 12 "b")/(7"a" + 12"b" - 7"a" + 12"b") = (7"c" + 12"d" + 7"c" - 12"d")/(7"c" + 12"d" - 7"c" + 12"d")`


`=> (14"a")/(24"b") = (14"c")/(24"d")`

Dividing both sides by  `14/24`


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

Hence, proved.

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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: 2

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Solution If (7a + 12b)/(7c + 12d) Then Prove that A/B=C/D Concept: Componendo and Dividendo Properties.
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