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Find Two Numbers Such that the Mean Proportional Between Them is 14 and Third Proportional to Them is 112. - ICSE Class 10 - Mathematics

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Question

Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.

Solution

Let the required number be  a and b.

Given 14 is the mean proportional between a and b

=> a : 14 = 14 : b

=> ab = 196

`=> a = 196/b` ....(1)

Also given third proportional to a and b is 112

=> a : b = b : 112

=> b^2 = 112a ....(2)

Using (1) we have

`b^2 = 112 xx 196/b`

`b^3 = (14)^3 (2)^3`

b = 28

From (1)

a= 196/25 = 7

Thus the two number are 7 and 28

  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: 10

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Solution Find Two Numbers Such that the Mean Proportional Between Them is 14 and Third Proportional to Them is 112. Concept: Proportions.
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