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If X, Y, Z Are in Continued Proportion Prove that (X + Y)^2/(Y + Z)^2 = X/Z - ICSE Class 10 - Mathematics

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Question

If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`

Solution

∵ x, y, z are in continued proportion

`∴ x/y = y/z => y^2 = zx` ......(1)

`=> (x + y)/(y + z) = y/z`   (By alternendo)

`=> (x + y)^2/(y + z)^2 = y^2/z^2`     (squaring both sides)

`=> (x + y)^2/(y + z) = (zx)/z^2`    [from (1)]

`=> (x + y)^2/(y + z)^2 = x/y`

hence proved

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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: 22

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Solution If X, Y, Z Are in Continued Proportion Prove that (X + Y)^2/(Y + Z)^2 = X/Z Concept: Proportions.
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