Question

Find the mean proportional between 24 and 6 ???

Answer 1

Let the mean proportion between 24 and 6 be x,

          According to the question :

$\dfrac{24}{x} = \dfrac{x}{6}$

$\dfrac{24}{x} \times \dfrac{x}{24} = \dfrac{x}{6} \times \dfrac{x}{24}$

$1 = \dfrac{x^{2}}{6 \times 24}$

$1 \times 144 = x^{2}$

144 = x^2

- 12 or 12 = x

Mean proportion between two positive numbers cant be negative.

therefore, mean proportional mean between 24 and 6 is 12.

Answer 2

$\huge \bold {\mathfrak {hey}}$

$\huge \bold {Answer}$

$\boxed \bold {Note :-}$ The proportional numbers can't be negative.

➡️ Let the mean proportional as x



$= > \: \frac{24}{x} = \frac{x}{6}$




$= > \: \frac{24}{x} \times \frac{x}{24} = \: \frac{x}{6} \times \frac{x}{24}$



$= > \: 1 = \frac{ {x}^{2} }{6 \times 24}$



$= > \: \: 1 \times 144 \: = {x}^{2}$


$= > \: \: 144 \: = {x}^{2}$


$= > \: \: 12 = x$


Therefore,

The mean proportional between the 24 and 6 is 12.


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