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If (4a + 9b) (4c – 9d) = (4a – 9b) (4c + 9d), Prove That: A: B = C: D. - Mathematics

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Question

If (4a + 9b) (4c – 9d) = (4a – 9b) (4c + 9d), prove that: a: b = c: d.

Solution

Given `(4a + 9b)/(4a - 9b) = (4c + 9d)/(4c - 9d)`

Applying componendo and dividendo

`(4a + 9b + 4a - 9b)/(4a + 9b - 4a + 9b) = (4c + 9d + 4c - 9d)/(4c + 9d - 4c + 9d)`

`(8a)/(18b) = (8c)/(18d)`

`a/b = c/d`

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(D) | Q: 13 | Page no. 102
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Solution If (4a + 9b) (4c – 9d) = (4a – 9b) (4c + 9d), Prove That: A: B = C: D. Concept: Componendo and Dividendo Properties.
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