Question

find the mean proportional to 6 and 54

Answer 1

18 is the mean proportional of 6 and 54

Answer 2

The mean proportional to 6 and 54 is 18

Given :

The numbers 6 and 54

To find :

The mean proportional to 6 and 54

Solution :

Step 1 of 2 :

Form the equation

Let x be the mean proportional to 6 and 54

By the given condition

6 : x = x : 54

Step 2 of 2 :

Find mean proportional to 6 and 54

6 : x = x : 54

$\displaystyle \sf{ \implies \frac{6}{x} = \frac{x}{54} }$

$\displaystyle \sf{ \implies {x}^{2} = 6 \times 54 }$

$\displaystyle \sf{ \implies x = \sqrt{ 6 \times 54 }}$

$\displaystyle \sf{ \implies x = \sqrt{ 6 \times 6 \times 3 \times 3 }}$

$\displaystyle \sf{ \implies x = \sqrt{ {6}^{2} \times {3}^{2} }}$

$\displaystyle \sf{ \implies x = 6 \times 3}$

$\displaystyle \sf{ \implies x = 18}$

The mean proportional to 6 and 54 is 18

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