Question

the mean proportion between 1/2 and 128

Answer 1

mean proportion
a/b=b/c
b^2=ac
b^2=1/2×128
b^2=64
b=8
the mean proportion is 8

Answer 2

The mean proportion between 1/2 and 128 is 8

Given : The numbers 1/2 and 128

To find : The mean proportion

Solution :

Step 1 of 2 :

Write down the given numbers

The given numbers are 1/2 and 128

Step 2 of 2 :

Find the mean proportion

Let x be the mean proportion

So by the given condition

$\displaystyle \sf{ \frac{1}{2} : x = x : 128}$

$\displaystyle \sf{ \implies {x}^{2} = \frac{1}{2} \times 128}$

$\displaystyle \sf{ \implies {x}^{2} = 64}$

$\displaystyle \sf{ \implies x = \sqrt{64} }$

$\displaystyle \sf{ \implies x = 8}$

Hence the required mean proportion = 8

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