Question

IF 2,3,6,x ARE IN PROPORTION , THE VALUE OF x is _____?​

Answer 1

Given, that 2,3,6,x are in proportion.

☯we need to find the value of "x".

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As we know that,

$\star\;{\boxed{\frak{\pink{Product \:of\:means\:=\:Product\:of\;extremes\;}}}}$

Here,

• Product of means = 3 × 6 = 18
• Product of extremes = 2 × x = 2x

Putting the values,

$:\implies\sf 18 = 2x$

$:\implies\sf x= \cancel{\dfrac{18}{2}}$

$:\implies\sf x = 9$

$:\implies{\boxed{\frak{\purple{ x = 9}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\:value\:of\:x\:is\:{\bf{9}} \;}}}$

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Answer 2

Given :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 2, 3, 6, x are in proportion

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

To find :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Value of x?

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Solution :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf \dfrac{2}{3} = \dfrac{6}{x}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Cross multiplying;

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf\dfrac{2}{3}\nearrow\dfrac{6}{x}\:\;\Bigg|\:\dfrac{2}{3}\nwarrow\dfrac{6}{x}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 2 \times x = 3 \times 6$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf \: 2x = 18$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf \: x \: = \cancel\dfrac{18}{2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\purple{\sf{x ={\frak{ 9}}}}}}}\;$

$\therefore\:{\sf{The\:value\:of\:x\:is\: {\textsf{9}}.}}$