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If `A/B = C/D` Show that (A + B) : (C + D) = Sqrt(A^2 + B^2) : Sqrt(C^2 + D^2) - ICSE Class 10 - Mathematics

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Question

if `a/b = c/d`  show that `(a + b) : (c + d) = sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`

Solution

Let `a/b = c/d = k` (say)

`=> a = bk, c = dk

L.H.S = `(a + b)/(c + d)`

`= (bk + b)/(dk + d)`

`= (b(k + 1))/(d(k + 1))`

`= b/d`

R.H.S = `sqrt(a^2 + b^2)/sqrt(c^2 + d^2)`

`= sqrt((bk)^2 + b^2)/sqrt((dk)^2 + d^2)`

`=  sqrt(b^2(k^2 + 1))/sqrt(d^2(k^2 + 1))`

`= sqrt(b^2)/sqrt(d^2)`

= b/d

∴ L.H.S = R.H.S

  Is there an error in this question or solution?

APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7D | Q: 16

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Solution If `A/B = C/D` Show that (A + B) : (C + D) = Sqrt(A^2 + B^2) : Sqrt(C^2 + D^2) Concept: Ratios.
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