Question

14. The mean proportional between two numbers is 9 and the third proportional of the two numbers is 243. What is the larger of the two numbers?

Answer 1

The larger of the two numbers is 27

Solution:

Let a, b be the required numbers

The mean proportional between two numbers is 9

Mean proportional is:

$\sqrt{ab} = 9$

$ab = 9^2\\\\ab = 81\\\\a = \frac{81}{b}$

The third proportional of the two numbers is 243

We know that,

$c = \frac{b^2}{a}$

$c = \frac{b^2}{\frac{81}{b}}\\\\243 = b^3 \times \frac{1}{81}\\\\ b^3 = 243 \times 81\\\\b^3 = 19683\\\\b = 27$

Therefore,

$a = \frac{81}{27}\\\\a = 3$

Thus the two numbers are 3 and 27

Therefore, large of the two numbers is 27

Learn more:

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Answer 2

Answer:

This is the correct answer