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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

#### 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

#### Video TutorialsVIEW ALL [1]

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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