Question

The mean proportional of 8 and 32 is? ​

Answer 1

Answer:

20 is the mean proportional between 8 and 32.

Answer 2

The mean proportional of 8 and 32 is 16

Given :

The numbers 8 and 32

To find :

The mean proportional of 8 and 32

Solution :

Step 1 of 2 :

Assume the mean proportional of 8 and 32

Let x be the mean proportional of 8 and 32

So by the given condition

8 : x = x : 32

Step 2 of 2 :

Find the mean proportion

$\displaystyle \sf{ \frac{8}{x} = \frac{x}{32} }$

$\displaystyle \sf{ \implies {x}^{2} = 8 \times 32}$

$\displaystyle \sf{ \implies x = \sqrt{8 \times 32} }$

$\displaystyle \sf{ \implies x = \sqrt{256} }$

$\displaystyle \sf{ \implies x = 16}$

Hence mean proportional of 8 and 32 is 16

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