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Question Number 14384 by ajfour last updated on 31/May/17

Commented by ajfour last updated on 31/May/17

$o n l y f i n d S = x + y + z$ $i n t e r m s o f a, b, c w h i c h a r e$ $s i d e s o f △ A B C .$
Commented by RasheedSindhi last updated on 31/May/17

$This Question is closely related$ $You can't use 'macro parameter character #' in math mode$ $Same equations exist here!$
Commented by ajfour last updated on 31/May/17

$y e s, i a m s e a r c h i n g f o r r a t h e r$ $s i m p l e e x p e e s s i o n s o f x, y, a n d$ $z i n t e r m s o f a, b, a n d c .$ $o u t e r m o s t b o u n d a r y o f f i g u r e$ $i s a h e x a g o n o f s i d e l e n g t h s$ $a, b, c, a, b, c a n d i n t h e s a m e$ $o r d e r .$
Commented by RasheedSindhi last updated on 31/May/17

$∠ {CA}^{'} B = 120 °$ $According to cosine law$ $a^{2} = x^{2} + y^{2} - 2 xy \cos ∠ {CA}^{'} B$ $a^{2} = x^{2} + y^{2} - 2 xy \cos 120$ $a^{2} = x^{2} + y^{2} - 2 xy (- 1 / 2)$ $a^{2} = x^{2} + y^{2} + xy$ $In a similar manner the remaining$ $two equtions can be obtained .$
Commented by mrW1 last updated on 31/May/17

$v e r y i n t e r e s t i n g t r y!$ $g e o m e t r i c s o l u t i o n s a r e t h e m o s t$ $b e a u t i f u l s o l u t i o n s, b e c a u s e y o u$ $c a n s e e a n d f e e l t h e m .$
Commented by RasheedSindhi last updated on 31/May/17

$N i c e S a y S i r!$
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