Determine distance between opposite corners of a cubic room of dimention x units.


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Question Number 6054 by Rasheed Soomro last updated on 11/Jun/16

$D e t e r m i n e d i s t a n c e b e t w e e n$ $o p p o s i t e c o r n e r s o f a c u b i c$ $r o o m o f d i m e n t i o n x u n i t s .$
Commented by Yozzii last updated on 11/Jun/16

$l e n g t h o f d i a g o n a l o n o n e f a c e = x \sqrt{2} u n i t s$ $B y P h y t h a g o r e a n t h e o r e m, r e q u i r e d d i s t a n c e = \sqrt{{(x \sqrt{2})}^{2} + x^{2}} = x \sqrt{3}$ $I n 3 D c o o r d i n a t e s l e t o n e v e r t e x b e t h e o r i g i n$ $a n d a n o p p o s i t e v e r t e x b e (\begin{matrix} x \\ x \\ x \end{matrix}) .$ $\Rightarrow∣ (\begin{matrix} x \\ x \\ x \end{matrix}) ∣= \sqrt{x^{2} + x^{2} + x^{2}} = x \sqrt{3} .$
Commented by Rasheed Soomro last updated on 11/Jun/16

${Th}^{a} nkS!$
	Answered by Yozzii last updated on 11/Jun/16

	$x \sqrt{3}$
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