Question

Find the mean proportional of 24 and 96.

Answer 1

The mean proportional between 24 and 96 is 48

Given :

The numbers 24 and 96

To find :

The mean proportional between 24 and 96

Solution :

Step 1 of 2 :

Form the equation

Let x be the mean proportional between 24 and 96

By the given condition

24 : x = x : 96

Step 2 of 2 :

Find the number

$\displaystyle \sf{24 : x = x : 96 }$

$\displaystyle \sf{ \implies \frac{24}{x} = \frac{x}{96} }$

$\displaystyle \sf{ \implies {x}^{2} = 24 \times 96}$

$\displaystyle \sf{ \implies x = \sqrt{24 \times 96}}$

$\displaystyle \sf{ \implies x = \sqrt{2304} }$

$\displaystyle \sf{ \implies x = \sqrt{ {48}^{2} } }$

$\displaystyle \sf{ \implies x = 48}$

Hence mean proportional between 24 and 96 is 48

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