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Find Two Numbers Such that the Mean Mean Proportional Between Them is 12 and the Third Proportional to Them is 96. - Mathematics

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Question

Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.

Solution

Let a and b be the two numbers whose mean proportional is 12

`∴ ab = 12^2 => ab = 144 => 144/a` ....(1)

Now third proportional is 96

∴ a : b : : b : 96

`=> b^2 = 96a`

`=> (144/a)^2 = 96a`

`=> a^3 = (144 xx 144)/96`

`=> a^3 = 216` 

`=> a = 6`

`b = 144/6 = 24`

Therefore the number are 6 and 24.

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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(B) | Q: 14 | Page no. 94
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Find Two Numbers Such that the Mean Mean Proportional Between Them is 12 and the Third Proportional to Them is 96. Concept: Proportions.
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