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If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d), Prove that A: B = C: D. - Mathematics

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Question

If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d), prove that a: b = c: d.

Solution

Given  `(7a + 8b)/(7c – 8d) = (7a – 8b)/(7c + 8d)`

Applying componendo and dividendo

`(7a + 8b + 7a - 8b)/(7a + 8b - 7 + 8b) = (7c + 8d + 7c - 8d)/(7c + 8d - 7c - 8d)`

`=> (14a)/(16b) = (14c)/(16d)`

`=> a/b = c/d`

Hence 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(C) | Q: 5 | Page no. 101
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Solution If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d), Prove that A: B = C: D. Concept: Componendo and Dividendo Properties.
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